Restriction of the Fourier Transform to Some Oscillating Curves
Abstract Let %$\phi %$ be a smooth function on a compact interval I. Let γ(t)=t,t2,…,tn-1,ϕ(t).%$\begin{aligned} \gamma (t)=\left( t,t^2,\ldots ,t^{n-1},\phi (t)\right) . \end{aligned}%$In this paper, we show that ∫I|f^(γ(t))|q|ϕ(n)(t)|2n(n+1)dt1/q≤C‖f‖Lp(Rn)%$\begin{aligned} \left( \int _I \big |\h...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Chen, Xianghong [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2017 |
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| Schlagwörter: |
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| Anmerkung: |
© Springer Science+Business Media, LLC 2017 |
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| Übergeordnetes Werk: |
Enthalten in: The journal of Fourier analysis and applications - Cambridge, Mass. : Birkhäuser Boston, 1994, 24(2017), 4 vom: 05. Juli, Seite 1141-1159 |
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| Übergeordnetes Werk: |
volume:24 ; year:2017 ; number:4 ; day:05 ; month:07 ; pages:1141-1159 |
| Links: |
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| DOI / URN: |
10.1007/s00041-017-9554-6 |
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| Katalog-ID: |
SPR000379689 |
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| 245 | 1 | 0 | |a Restriction of the Fourier Transform to Some Oscillating Curves |
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| 520 | |a Abstract Let %$\phi %$ be a smooth function on a compact interval I. Let γ(t)=t,t2,…,tn-1,ϕ(t).%$\begin{aligned} \gamma (t)=\left( t,t^2,\ldots ,t^{n-1},\phi (t)\right) . \end{aligned}%$In this paper, we show that ∫I|f^(γ(t))|q|ϕ(n)(t)|2n(n+1)dt1/q≤C‖f‖Lp(Rn)%$\begin{aligned} \left( \int _I \big |\hat{f}(\gamma (t))\big |^q \big |\phi ^{(n)}(t)\big |^{\frac{2}{n(n+1)}} \mathrm{{d}}t\right) ^{1/q}\le C\Vert f\Vert _{L^p(\mathbb R^n)} \end{aligned}%$holds in the range 1≤p<n2+n+2n2+n,1≤q<2n2+np′.%$\begin{aligned} 1\le p<\frac{n^2+n+2}{n^2+n},\quad 1\le q<\frac{2}{n^2+n}p'. \end{aligned}%$This generalizes an affine restriction theorem of Sjölin (Stud Math 51:169–182, 1974) for %$n=2%$. Our proof relies on ideas of Sjölin (Stud Math 51:169–182, 1974) and Drury (Ann Inst Fourier (Grenoble) 35(1):117–123, 1985), and more recently Bak, Oberlin and Seeger (J Aust Math Soc 85(1):1–28, 2008) and Stovall (Am J Math 138(2):449–471, 2016), as well as a variation bound for smooth functions. | ||
| 650 | 4 | |a Fourier restriction |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Affine arclength measure |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Oscillating curve |7 (dpeaa)DE-He213 | |
| 700 | 1 | |a Fan, Dashan |4 aut | |
| 700 | 1 | |a Wang, Lifeng |4 aut | |
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10.1007/s00041-017-9554-6 doi (DE-627)SPR000379689 (SPR)s00041-017-9554-6-e DE-627 ger DE-627 rakwb eng Chen, Xianghong verfasserin aut Restriction of the Fourier Transform to Some Oscillating Curves 2017 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer Science+Business Media, LLC 2017 Abstract Let %$\phi %$ be a smooth function on a compact interval I. Let γ(t)=t,t2,…,tn-1,ϕ(t).%$\begin{aligned} \gamma (t)=\left( t,t^2,\ldots ,t^{n-1},\phi (t)\right) . \end{aligned}%$In this paper, we show that ∫I|f^(γ(t))|q|ϕ(n)(t)|2n(n+1)dt1/q≤C‖f‖Lp(Rn)%$\begin{aligned} \left( \int _I \big |\hat{f}(\gamma (t))\big |^q \big |\phi ^{(n)}(t)\big |^{\frac{2}{n(n+1)}} \mathrm{{d}}t\right) ^{1/q}\le C\Vert f\Vert _{L^p(\mathbb R^n)} \end{aligned}%$holds in the range 1≤p<n2+n+2n2+n,1≤q<2n2+np′.%$\begin{aligned} 1\le p<\frac{n^2+n+2}{n^2+n},\quad 1\le q<\frac{2}{n^2+n}p'. \end{aligned}%$This generalizes an affine restriction theorem of Sjölin (Stud Math 51:169–182, 1974) for %$n=2%$. Our proof relies on ideas of Sjölin (Stud Math 51:169–182, 1974) and Drury (Ann Inst Fourier (Grenoble) 35(1):117–123, 1985), and more recently Bak, Oberlin and Seeger (J Aust Math Soc 85(1):1–28, 2008) and Stovall (Am J Math 138(2):449–471, 2016), as well as a variation bound for smooth functions. Fourier restriction (dpeaa)DE-He213 Affine arclength measure (dpeaa)DE-He213 Oscillating curve (dpeaa)DE-He213 Fan, Dashan aut Wang, Lifeng aut Enthalten in The journal of Fourier analysis and applications Cambridge, Mass. : Birkhäuser Boston, 1994 24(2017), 4 vom: 05. Juli, Seite 1141-1159 (DE-627)326360484 (DE-600)2042054-7 1531-5851 nnns volume:24 year:2017 number:4 day:05 month:07 pages:1141-1159 https://dx.doi.org/10.1007/s00041-017-9554-6 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 24 2017 4 05 07 1141-1159 |
| spelling |
10.1007/s00041-017-9554-6 doi (DE-627)SPR000379689 (SPR)s00041-017-9554-6-e DE-627 ger DE-627 rakwb eng Chen, Xianghong verfasserin aut Restriction of the Fourier Transform to Some Oscillating Curves 2017 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer Science+Business Media, LLC 2017 Abstract Let %$\phi %$ be a smooth function on a compact interval I. Let γ(t)=t,t2,…,tn-1,ϕ(t).%$\begin{aligned} \gamma (t)=\left( t,t^2,\ldots ,t^{n-1},\phi (t)\right) . \end{aligned}%$In this paper, we show that ∫I|f^(γ(t))|q|ϕ(n)(t)|2n(n+1)dt1/q≤C‖f‖Lp(Rn)%$\begin{aligned} \left( \int _I \big |\hat{f}(\gamma (t))\big |^q \big |\phi ^{(n)}(t)\big |^{\frac{2}{n(n+1)}} \mathrm{{d}}t\right) ^{1/q}\le C\Vert f\Vert _{L^p(\mathbb R^n)} \end{aligned}%$holds in the range 1≤p<n2+n+2n2+n,1≤q<2n2+np′.%$\begin{aligned} 1\le p<\frac{n^2+n+2}{n^2+n},\quad 1\le q<\frac{2}{n^2+n}p'. \end{aligned}%$This generalizes an affine restriction theorem of Sjölin (Stud Math 51:169–182, 1974) for %$n=2%$. Our proof relies on ideas of Sjölin (Stud Math 51:169–182, 1974) and Drury (Ann Inst Fourier (Grenoble) 35(1):117–123, 1985), and more recently Bak, Oberlin and Seeger (J Aust Math Soc 85(1):1–28, 2008) and Stovall (Am J Math 138(2):449–471, 2016), as well as a variation bound for smooth functions. Fourier restriction (dpeaa)DE-He213 Affine arclength measure (dpeaa)DE-He213 Oscillating curve (dpeaa)DE-He213 Fan, Dashan aut Wang, Lifeng aut Enthalten in The journal of Fourier analysis and applications Cambridge, Mass. : Birkhäuser Boston, 1994 24(2017), 4 vom: 05. Juli, Seite 1141-1159 (DE-627)326360484 (DE-600)2042054-7 1531-5851 nnns volume:24 year:2017 number:4 day:05 month:07 pages:1141-1159 https://dx.doi.org/10.1007/s00041-017-9554-6 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 24 2017 4 05 07 1141-1159 |
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10.1007/s00041-017-9554-6 doi (DE-627)SPR000379689 (SPR)s00041-017-9554-6-e DE-627 ger DE-627 rakwb eng Chen, Xianghong verfasserin aut Restriction of the Fourier Transform to Some Oscillating Curves 2017 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer Science+Business Media, LLC 2017 Abstract Let %$\phi %$ be a smooth function on a compact interval I. Let γ(t)=t,t2,…,tn-1,ϕ(t).%$\begin{aligned} \gamma (t)=\left( t,t^2,\ldots ,t^{n-1},\phi (t)\right) . \end{aligned}%$In this paper, we show that ∫I|f^(γ(t))|q|ϕ(n)(t)|2n(n+1)dt1/q≤C‖f‖Lp(Rn)%$\begin{aligned} \left( \int _I \big |\hat{f}(\gamma (t))\big |^q \big |\phi ^{(n)}(t)\big |^{\frac{2}{n(n+1)}} \mathrm{{d}}t\right) ^{1/q}\le C\Vert f\Vert _{L^p(\mathbb R^n)} \end{aligned}%$holds in the range 1≤p<n2+n+2n2+n,1≤q<2n2+np′.%$\begin{aligned} 1\le p<\frac{n^2+n+2}{n^2+n},\quad 1\le q<\frac{2}{n^2+n}p'. \end{aligned}%$This generalizes an affine restriction theorem of Sjölin (Stud Math 51:169–182, 1974) for %$n=2%$. Our proof relies on ideas of Sjölin (Stud Math 51:169–182, 1974) and Drury (Ann Inst Fourier (Grenoble) 35(1):117–123, 1985), and more recently Bak, Oberlin and Seeger (J Aust Math Soc 85(1):1–28, 2008) and Stovall (Am J Math 138(2):449–471, 2016), as well as a variation bound for smooth functions. Fourier restriction (dpeaa)DE-He213 Affine arclength measure (dpeaa)DE-He213 Oscillating curve (dpeaa)DE-He213 Fan, Dashan aut Wang, Lifeng aut Enthalten in The journal of Fourier analysis and applications Cambridge, Mass. : Birkhäuser Boston, 1994 24(2017), 4 vom: 05. Juli, Seite 1141-1159 (DE-627)326360484 (DE-600)2042054-7 1531-5851 nnns volume:24 year:2017 number:4 day:05 month:07 pages:1141-1159 https://dx.doi.org/10.1007/s00041-017-9554-6 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 24 2017 4 05 07 1141-1159 |
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10.1007/s00041-017-9554-6 doi (DE-627)SPR000379689 (SPR)s00041-017-9554-6-e DE-627 ger DE-627 rakwb eng Chen, Xianghong verfasserin aut Restriction of the Fourier Transform to Some Oscillating Curves 2017 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer Science+Business Media, LLC 2017 Abstract Let %$\phi %$ be a smooth function on a compact interval I. Let γ(t)=t,t2,…,tn-1,ϕ(t).%$\begin{aligned} \gamma (t)=\left( t,t^2,\ldots ,t^{n-1},\phi (t)\right) . \end{aligned}%$In this paper, we show that ∫I|f^(γ(t))|q|ϕ(n)(t)|2n(n+1)dt1/q≤C‖f‖Lp(Rn)%$\begin{aligned} \left( \int _I \big |\hat{f}(\gamma (t))\big |^q \big |\phi ^{(n)}(t)\big |^{\frac{2}{n(n+1)}} \mathrm{{d}}t\right) ^{1/q}\le C\Vert f\Vert _{L^p(\mathbb R^n)} \end{aligned}%$holds in the range 1≤p<n2+n+2n2+n,1≤q<2n2+np′.%$\begin{aligned} 1\le p<\frac{n^2+n+2}{n^2+n},\quad 1\le q<\frac{2}{n^2+n}p'. \end{aligned}%$This generalizes an affine restriction theorem of Sjölin (Stud Math 51:169–182, 1974) for %$n=2%$. Our proof relies on ideas of Sjölin (Stud Math 51:169–182, 1974) and Drury (Ann Inst Fourier (Grenoble) 35(1):117–123, 1985), and more recently Bak, Oberlin and Seeger (J Aust Math Soc 85(1):1–28, 2008) and Stovall (Am J Math 138(2):449–471, 2016), as well as a variation bound for smooth functions. Fourier restriction (dpeaa)DE-He213 Affine arclength measure (dpeaa)DE-He213 Oscillating curve (dpeaa)DE-He213 Fan, Dashan aut Wang, Lifeng aut Enthalten in The journal of Fourier analysis and applications Cambridge, Mass. : Birkhäuser Boston, 1994 24(2017), 4 vom: 05. Juli, Seite 1141-1159 (DE-627)326360484 (DE-600)2042054-7 1531-5851 nnns volume:24 year:2017 number:4 day:05 month:07 pages:1141-1159 https://dx.doi.org/10.1007/s00041-017-9554-6 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 24 2017 4 05 07 1141-1159 |
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10.1007/s00041-017-9554-6 doi (DE-627)SPR000379689 (SPR)s00041-017-9554-6-e DE-627 ger DE-627 rakwb eng Chen, Xianghong verfasserin aut Restriction of the Fourier Transform to Some Oscillating Curves 2017 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer Science+Business Media, LLC 2017 Abstract Let %$\phi %$ be a smooth function on a compact interval I. Let γ(t)=t,t2,…,tn-1,ϕ(t).%$\begin{aligned} \gamma (t)=\left( t,t^2,\ldots ,t^{n-1},\phi (t)\right) . \end{aligned}%$In this paper, we show that ∫I|f^(γ(t))|q|ϕ(n)(t)|2n(n+1)dt1/q≤C‖f‖Lp(Rn)%$\begin{aligned} \left( \int _I \big |\hat{f}(\gamma (t))\big |^q \big |\phi ^{(n)}(t)\big |^{\frac{2}{n(n+1)}} \mathrm{{d}}t\right) ^{1/q}\le C\Vert f\Vert _{L^p(\mathbb R^n)} \end{aligned}%$holds in the range 1≤p<n2+n+2n2+n,1≤q<2n2+np′.%$\begin{aligned} 1\le p<\frac{n^2+n+2}{n^2+n},\quad 1\le q<\frac{2}{n^2+n}p'. \end{aligned}%$This generalizes an affine restriction theorem of Sjölin (Stud Math 51:169–182, 1974) for %$n=2%$. Our proof relies on ideas of Sjölin (Stud Math 51:169–182, 1974) and Drury (Ann Inst Fourier (Grenoble) 35(1):117–123, 1985), and more recently Bak, Oberlin and Seeger (J Aust Math Soc 85(1):1–28, 2008) and Stovall (Am J Math 138(2):449–471, 2016), as well as a variation bound for smooth functions. Fourier restriction (dpeaa)DE-He213 Affine arclength measure (dpeaa)DE-He213 Oscillating curve (dpeaa)DE-He213 Fan, Dashan aut Wang, Lifeng aut Enthalten in The journal of Fourier analysis and applications Cambridge, Mass. : Birkhäuser Boston, 1994 24(2017), 4 vom: 05. Juli, Seite 1141-1159 (DE-627)326360484 (DE-600)2042054-7 1531-5851 nnns volume:24 year:2017 number:4 day:05 month:07 pages:1141-1159 https://dx.doi.org/10.1007/s00041-017-9554-6 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 24 2017 4 05 07 1141-1159 |
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Let γ(t)=t,t2,…,tn-1,ϕ(t).%$\begin{aligned} \gamma (t)=\left( t,t^2,\ldots ,t^{n-1},\phi (t)\right) . \end{aligned}%$In this paper, we show that ∫I|f^(γ(t))|q|ϕ(n)(t)|2n(n+1)dt1/q≤C‖f‖Lp(Rn)%$\begin{aligned} \left( \int _I \big |\hat{f}(\gamma (t))\big |^q \big |\phi ^{(n)}(t)\big |^{\frac{2}{n(n+1)}} \mathrm{{d}}t\right) ^{1/q}\le C\Vert f\Vert _{L^p(\mathbb R^n)} \end{aligned}%$holds in the range 1≤p<n2+n+2n2+n,1≤q<2n2+np′.%$\begin{aligned} 1\le p<\frac{n^2+n+2}{n^2+n},\quad 1\le q<\frac{2}{n^2+n}p'. \end{aligned}%$This generalizes an affine restriction theorem of Sjölin (Stud Math 51:169–182, 1974) for %$n=2%$. Our proof relies on ideas of Sjölin (Stud Math 51:169–182, 1974) and Drury (Ann Inst Fourier (Grenoble) 35(1):117–123, 1985), and more recently Bak, Oberlin and Seeger (J Aust Math Soc 85(1):1–28, 2008) and Stovall (Am J Math 138(2):449–471, 2016), as well as a variation bound for smooth functions.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Fourier restriction</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Affine arclength measure</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Oscillating curve</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Fan, Dashan</subfield><subfield code="4">aut</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Wang, Lifeng</subfield><subfield code="4">aut</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">The journal of Fourier analysis and applications</subfield><subfield code="d">Cambridge, Mass. : Birkhäuser Boston, 1994</subfield><subfield code="g">24(2017), 4 vom: 05. 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Chen, Xianghong |
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Chen, Xianghong misc Fourier restriction misc Affine arclength measure misc Oscillating curve Restriction of the Fourier Transform to Some Oscillating Curves |
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Restriction of the Fourier Transform to Some Oscillating Curves Fourier restriction (dpeaa)DE-He213 Affine arclength measure (dpeaa)DE-He213 Oscillating curve (dpeaa)DE-He213 |
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Restriction of the Fourier Transform to Some Oscillating Curves |
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restriction of the fourier transform to some oscillating curves |
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Restriction of the Fourier Transform to Some Oscillating Curves |
| abstract |
Abstract Let %$\phi %$ be a smooth function on a compact interval I. Let γ(t)=t,t2,…,tn-1,ϕ(t).%$\begin{aligned} \gamma (t)=\left( t,t^2,\ldots ,t^{n-1},\phi (t)\right) . \end{aligned}%$In this paper, we show that ∫I|f^(γ(t))|q|ϕ(n)(t)|2n(n+1)dt1/q≤C‖f‖Lp(Rn)%$\begin{aligned} \left( \int _I \big |\hat{f}(\gamma (t))\big |^q \big |\phi ^{(n)}(t)\big |^{\frac{2}{n(n+1)}} \mathrm{{d}}t\right) ^{1/q}\le C\Vert f\Vert _{L^p(\mathbb R^n)} \end{aligned}%$holds in the range 1≤p<n2+n+2n2+n,1≤q<2n2+np′.%$\begin{aligned} 1\le p<\frac{n^2+n+2}{n^2+n},\quad 1\le q<\frac{2}{n^2+n}p'. \end{aligned}%$This generalizes an affine restriction theorem of Sjölin (Stud Math 51:169–182, 1974) for %$n=2%$. Our proof relies on ideas of Sjölin (Stud Math 51:169–182, 1974) and Drury (Ann Inst Fourier (Grenoble) 35(1):117–123, 1985), and more recently Bak, Oberlin and Seeger (J Aust Math Soc 85(1):1–28, 2008) and Stovall (Am J Math 138(2):449–471, 2016), as well as a variation bound for smooth functions. © Springer Science+Business Media, LLC 2017 |
| abstractGer |
Abstract Let %$\phi %$ be a smooth function on a compact interval I. Let γ(t)=t,t2,…,tn-1,ϕ(t).%$\begin{aligned} \gamma (t)=\left( t,t^2,\ldots ,t^{n-1},\phi (t)\right) . \end{aligned}%$In this paper, we show that ∫I|f^(γ(t))|q|ϕ(n)(t)|2n(n+1)dt1/q≤C‖f‖Lp(Rn)%$\begin{aligned} \left( \int _I \big |\hat{f}(\gamma (t))\big |^q \big |\phi ^{(n)}(t)\big |^{\frac{2}{n(n+1)}} \mathrm{{d}}t\right) ^{1/q}\le C\Vert f\Vert _{L^p(\mathbb R^n)} \end{aligned}%$holds in the range 1≤p<n2+n+2n2+n,1≤q<2n2+np′.%$\begin{aligned} 1\le p<\frac{n^2+n+2}{n^2+n},\quad 1\le q<\frac{2}{n^2+n}p'. \end{aligned}%$This generalizes an affine restriction theorem of Sjölin (Stud Math 51:169–182, 1974) for %$n=2%$. Our proof relies on ideas of Sjölin (Stud Math 51:169–182, 1974) and Drury (Ann Inst Fourier (Grenoble) 35(1):117–123, 1985), and more recently Bak, Oberlin and Seeger (J Aust Math Soc 85(1):1–28, 2008) and Stovall (Am J Math 138(2):449–471, 2016), as well as a variation bound for smooth functions. © Springer Science+Business Media, LLC 2017 |
| abstract_unstemmed |
Abstract Let %$\phi %$ be a smooth function on a compact interval I. Let γ(t)=t,t2,…,tn-1,ϕ(t).%$\begin{aligned} \gamma (t)=\left( t,t^2,\ldots ,t^{n-1},\phi (t)\right) . \end{aligned}%$In this paper, we show that ∫I|f^(γ(t))|q|ϕ(n)(t)|2n(n+1)dt1/q≤C‖f‖Lp(Rn)%$\begin{aligned} \left( \int _I \big |\hat{f}(\gamma (t))\big |^q \big |\phi ^{(n)}(t)\big |^{\frac{2}{n(n+1)}} \mathrm{{d}}t\right) ^{1/q}\le C\Vert f\Vert _{L^p(\mathbb R^n)} \end{aligned}%$holds in the range 1≤p<n2+n+2n2+n,1≤q<2n2+np′.%$\begin{aligned} 1\le p<\frac{n^2+n+2}{n^2+n},\quad 1\le q<\frac{2}{n^2+n}p'. \end{aligned}%$This generalizes an affine restriction theorem of Sjölin (Stud Math 51:169–182, 1974) for %$n=2%$. Our proof relies on ideas of Sjölin (Stud Math 51:169–182, 1974) and Drury (Ann Inst Fourier (Grenoble) 35(1):117–123, 1985), and more recently Bak, Oberlin and Seeger (J Aust Math Soc 85(1):1–28, 2008) and Stovall (Am J Math 138(2):449–471, 2016), as well as a variation bound for smooth functions. © Springer Science+Business Media, LLC 2017 |
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Restriction of the Fourier Transform to Some Oscillating Curves |
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Fan, Dashan Wang, Lifeng |
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2024-07-03T15:40:47.380Z |
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|
| score |
7.399865 |