Weighted Morrey Spaces Related to Certain Nonnegative Potentials and Riesz Transforms

Let L=-Δ+V be a Schrödinger operator, where Δ is the Laplacian on Rd and the nonnegative potential V belongs to the reverse Hölder class RHq for q≥d. The Riesz transform associated with the operator L=-Δ+V is denoted by R=∇(-Δ+V)-1/2 and the dual Riesz transform is denoted by R⁎=(-Δ+V)-1/2∇. In this...
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Autor*in:	Hua Wang [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2019

Übergeordnetes Werk:	In: Journal of Function Spaces - Hindawi Limited, 2016, (2019)
Übergeordnetes Werk:	year:2019

Links:	Link aufrufen Link aufrufen Link aufrufen Journal toc Journal toc

DOI / URN:	10.1155/2019/7057512

Katalog-ID:	DOAJ046655735

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520			\|a Let L=-Δ+V be a Schrödinger operator, where Δ is the Laplacian on Rd and the nonnegative potential V belongs to the reverse Hölder class RHq for q≥d. The Riesz transform associated with the operator L=-Δ+V is denoted by R=∇(-Δ+V)-1/2 and the dual Riesz transform is denoted by R⁎=(-Δ+V)-1/2∇. In this paper, we first introduce some kinds of weighted Morrey spaces related to certain nonnegative potentials belonging to the reverse Hölder class RHq for q≥d. Then we will establish the mapping properties of the operator R and its adjoint R⁎ on these new spaces. Furthermore, the weighted strong-type estimate and weighted endpoint estimate for the corresponding commutators [b,R] and [b,R⁎] are also obtained. The classes of weights, classes of symbol functions, and weighted Morrey spaces discussed in this paper are larger than Ap, BMO(Rd), and Lp,κ(w) corresponding to the classical Riesz transforms (V≡0).
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912			\|a GBV_ILN_63
912			\|a GBV_ILN_65
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912			\|a GBV_ILN_70
912			\|a GBV_ILN_73
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912			\|a GBV_ILN_110
912			\|a GBV_ILN_151
912			\|a GBV_ILN_161
912			\|a GBV_ILN_170
912			\|a GBV_ILN_171
912			\|a GBV_ILN_206
912			\|a GBV_ILN_213
912			\|a GBV_ILN_224
912			\|a GBV_ILN_230
912			\|a GBV_ILN_285
912			\|a GBV_ILN_293
912			\|a GBV_ILN_370
912			\|a GBV_ILN_602
912			\|a GBV_ILN_636
912			\|a GBV_ILN_702
912			\|a GBV_ILN_2001
912			\|a GBV_ILN_2003
912			\|a GBV_ILN_2004
912			\|a GBV_ILN_2005
912			\|a GBV_ILN_2006
912			\|a GBV_ILN_2007
912			\|a GBV_ILN_2008
912			\|a GBV_ILN_2009
912			\|a GBV_ILN_2010
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912			\|a GBV_ILN_2015
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912			\|a GBV_ILN_2025
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912			\|a GBV_ILN_2027
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912			\|a GBV_ILN_2037
912			\|a GBV_ILN_2038
912			\|a GBV_ILN_2044
912			\|a GBV_ILN_2048
912			\|a GBV_ILN_2050
912			\|a GBV_ILN_2055
912			\|a GBV_ILN_2056
912			\|a GBV_ILN_2057
912			\|a GBV_ILN_2059
912			\|a GBV_ILN_2061
912			\|a GBV_ILN_2068
912			\|a GBV_ILN_2088
912			\|a GBV_ILN_2106
912			\|a GBV_ILN_2108
912			\|a GBV_ILN_2111
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912			\|a GBV_ILN_2144
912			\|a GBV_ILN_2147
912			\|a GBV_ILN_2148
912			\|a GBV_ILN_2152
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912			\|a GBV_ILN_2336
912			\|a GBV_ILN_2470
912			\|a GBV_ILN_2507
912			\|a GBV_ILN_2522
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912			\|a GBV_ILN_4035
912			\|a GBV_ILN_4037
912			\|a GBV_ILN_4046
912			\|a GBV_ILN_4112
912			\|a GBV_ILN_4125
912			\|a GBV_ILN_4126
912			\|a GBV_ILN_4242
912			\|a GBV_ILN_4249
912			\|a GBV_ILN_4251
912			\|a GBV_ILN_4305
912			\|a GBV_ILN_4306
912			\|a GBV_ILN_4307
912			\|a GBV_ILN_4313
912			\|a GBV_ILN_4322
912			\|a GBV_ILN_4323
912			\|a GBV_ILN_4324
912			\|a GBV_ILN_4325
912			\|a GBV_ILN_4326
912			\|a GBV_ILN_4333
912			\|a GBV_ILN_4334
912			\|a GBV_ILN_4335
912			\|a GBV_ILN_4336
912			\|a GBV_ILN_4338
912			\|a GBV_ILN_4367
912			\|a GBV_ILN_4700
951			\|a AR
952			\|j 2019

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publishDate	2019
allfields	10.1155/2019/7057512 doi (DE-627)DOAJ046655735 (DE-599)DOAJ1660d5dda7b94d5586d16b23e732be1a DE-627 ger DE-627 rakwb eng QA1-939 Hua Wang verfasserin aut Weighted Morrey Spaces Related to Certain Nonnegative Potentials and Riesz Transforms 2019 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Let L=-Δ+V be a Schrödinger operator, where Δ is the Laplacian on Rd and the nonnegative potential V belongs to the reverse Hölder class RHq for q≥d. The Riesz transform associated with the operator L=-Δ+V is denoted by R=∇(-Δ+V)-1/2 and the dual Riesz transform is denoted by R⁎=(-Δ+V)-1/2∇. In this paper, we first introduce some kinds of weighted Morrey spaces related to certain nonnegative potentials belonging to the reverse Hölder class RHq for q≥d. Then we will establish the mapping properties of the operator R and its adjoint R⁎ on these new spaces. Furthermore, the weighted strong-type estimate and weighted endpoint estimate for the corresponding commutators [b,R] and [b,R⁎] are also obtained. The classes of weights, classes of symbol functions, and weighted Morrey spaces discussed in this paper are larger than Ap, BMO(Rd), and Lp,κ(w) corresponding to the classical Riesz transforms (V≡0). Mathematics In Journal of Function Spaces Hindawi Limited, 2016 (2019) (DE-627)862936489 (DE-600)2861541-4 23148888 nnns year:2019 https://doi.org/10.1155/2019/7057512 kostenfrei https://doaj.org/article/1660d5dda7b94d5586d16b23e732be1a kostenfrei http://dx.doi.org/10.1155/2019/7057512 kostenfrei https://doaj.org/toc/2314-8896 Journal toc kostenfrei https://doaj.org/toc/2314-8888 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ SSG-OLC-PHA GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 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_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2106 GBV_ILN_2108 GBV_ILN_2111 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 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_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 2019
spelling	10.1155/2019/7057512 doi (DE-627)DOAJ046655735 (DE-599)DOAJ1660d5dda7b94d5586d16b23e732be1a DE-627 ger DE-627 rakwb eng QA1-939 Hua Wang verfasserin aut Weighted Morrey Spaces Related to Certain Nonnegative Potentials and Riesz Transforms 2019 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Let L=-Δ+V be a Schrödinger operator, where Δ is the Laplacian on Rd and the nonnegative potential V belongs to the reverse Hölder class RHq for q≥d. The Riesz transform associated with the operator L=-Δ+V is denoted by R=∇(-Δ+V)-1/2 and the dual Riesz transform is denoted by R⁎=(-Δ+V)-1/2∇. In this paper, we first introduce some kinds of weighted Morrey spaces related to certain nonnegative potentials belonging to the reverse Hölder class RHq for q≥d. Then we will establish the mapping properties of the operator R and its adjoint R⁎ on these new spaces. Furthermore, the weighted strong-type estimate and weighted endpoint estimate for the corresponding commutators [b,R] and [b,R⁎] are also obtained. The classes of weights, classes of symbol functions, and weighted Morrey spaces discussed in this paper are larger than Ap, BMO(Rd), and Lp,κ(w) corresponding to the classical Riesz transforms (V≡0). Mathematics In Journal of Function Spaces Hindawi Limited, 2016 (2019) (DE-627)862936489 (DE-600)2861541-4 23148888 nnns year:2019 https://doi.org/10.1155/2019/7057512 kostenfrei https://doaj.org/article/1660d5dda7b94d5586d16b23e732be1a kostenfrei http://dx.doi.org/10.1155/2019/7057512 kostenfrei https://doaj.org/toc/2314-8896 Journal toc kostenfrei https://doaj.org/toc/2314-8888 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ SSG-OLC-PHA GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 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_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2106 GBV_ILN_2108 GBV_ILN_2111 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 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_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 2019
allfields_unstemmed	10.1155/2019/7057512 doi (DE-627)DOAJ046655735 (DE-599)DOAJ1660d5dda7b94d5586d16b23e732be1a DE-627 ger DE-627 rakwb eng QA1-939 Hua Wang verfasserin aut Weighted Morrey Spaces Related to Certain Nonnegative Potentials and Riesz Transforms 2019 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Let L=-Δ+V be a Schrödinger operator, where Δ is the Laplacian on Rd and the nonnegative potential V belongs to the reverse Hölder class RHq for q≥d. The Riesz transform associated with the operator L=-Δ+V is denoted by R=∇(-Δ+V)-1/2 and the dual Riesz transform is denoted by R⁎=(-Δ+V)-1/2∇. In this paper, we first introduce some kinds of weighted Morrey spaces related to certain nonnegative potentials belonging to the reverse Hölder class RHq for q≥d. Then we will establish the mapping properties of the operator R and its adjoint R⁎ on these new spaces. Furthermore, the weighted strong-type estimate and weighted endpoint estimate for the corresponding commutators [b,R] and [b,R⁎] are also obtained. The classes of weights, classes of symbol functions, and weighted Morrey spaces discussed in this paper are larger than Ap, BMO(Rd), and Lp,κ(w) corresponding to the classical Riesz transforms (V≡0). Mathematics In Journal of Function Spaces Hindawi Limited, 2016 (2019) (DE-627)862936489 (DE-600)2861541-4 23148888 nnns year:2019 https://doi.org/10.1155/2019/7057512 kostenfrei https://doaj.org/article/1660d5dda7b94d5586d16b23e732be1a kostenfrei http://dx.doi.org/10.1155/2019/7057512 kostenfrei https://doaj.org/toc/2314-8896 Journal toc kostenfrei https://doaj.org/toc/2314-8888 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ SSG-OLC-PHA GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 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_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2106 GBV_ILN_2108 GBV_ILN_2111 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 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_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 2019
allfieldsGer	10.1155/2019/7057512 doi (DE-627)DOAJ046655735 (DE-599)DOAJ1660d5dda7b94d5586d16b23e732be1a DE-627 ger DE-627 rakwb eng QA1-939 Hua Wang verfasserin aut Weighted Morrey Spaces Related to Certain Nonnegative Potentials and Riesz Transforms 2019 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Let L=-Δ+V be a Schrödinger operator, where Δ is the Laplacian on Rd and the nonnegative potential V belongs to the reverse Hölder class RHq for q≥d. The Riesz transform associated with the operator L=-Δ+V is denoted by R=∇(-Δ+V)-1/2 and the dual Riesz transform is denoted by R⁎=(-Δ+V)-1/2∇. In this paper, we first introduce some kinds of weighted Morrey spaces related to certain nonnegative potentials belonging to the reverse Hölder class RHq for q≥d. Then we will establish the mapping properties of the operator R and its adjoint R⁎ on these new spaces. Furthermore, the weighted strong-type estimate and weighted endpoint estimate for the corresponding commutators [b,R] and [b,R⁎] are also obtained. The classes of weights, classes of symbol functions, and weighted Morrey spaces discussed in this paper are larger than Ap, BMO(Rd), and Lp,κ(w) corresponding to the classical Riesz transforms (V≡0). Mathematics In Journal of Function Spaces Hindawi Limited, 2016 (2019) (DE-627)862936489 (DE-600)2861541-4 23148888 nnns year:2019 https://doi.org/10.1155/2019/7057512 kostenfrei https://doaj.org/article/1660d5dda7b94d5586d16b23e732be1a kostenfrei http://dx.doi.org/10.1155/2019/7057512 kostenfrei https://doaj.org/toc/2314-8896 Journal toc kostenfrei https://doaj.org/toc/2314-8888 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ SSG-OLC-PHA GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 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_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2106 GBV_ILN_2108 GBV_ILN_2111 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 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_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 2019
allfieldsSound	10.1155/2019/7057512 doi (DE-627)DOAJ046655735 (DE-599)DOAJ1660d5dda7b94d5586d16b23e732be1a DE-627 ger DE-627 rakwb eng QA1-939 Hua Wang verfasserin aut Weighted Morrey Spaces Related to Certain Nonnegative Potentials and Riesz Transforms 2019 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Let L=-Δ+V be a Schrödinger operator, where Δ is the Laplacian on Rd and the nonnegative potential V belongs to the reverse Hölder class RHq for q≥d. The Riesz transform associated with the operator L=-Δ+V is denoted by R=∇(-Δ+V)-1/2 and the dual Riesz transform is denoted by R⁎=(-Δ+V)-1/2∇. In this paper, we first introduce some kinds of weighted Morrey spaces related to certain nonnegative potentials belonging to the reverse Hölder class RHq for q≥d. Then we will establish the mapping properties of the operator R and its adjoint R⁎ on these new spaces. Furthermore, the weighted strong-type estimate and weighted endpoint estimate for the corresponding commutators [b,R] and [b,R⁎] are also obtained. The classes of weights, classes of symbol functions, and weighted Morrey spaces discussed in this paper are larger than Ap, BMO(Rd), and Lp,κ(w) corresponding to the classical Riesz transforms (V≡0). Mathematics In Journal of Function Spaces Hindawi Limited, 2016 (2019) (DE-627)862936489 (DE-600)2861541-4 23148888 nnns year:2019 https://doi.org/10.1155/2019/7057512 kostenfrei https://doaj.org/article/1660d5dda7b94d5586d16b23e732be1a kostenfrei http://dx.doi.org/10.1155/2019/7057512 kostenfrei https://doaj.org/toc/2314-8896 Journal toc kostenfrei https://doaj.org/toc/2314-8888 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ SSG-OLC-PHA GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 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_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2106 GBV_ILN_2108 GBV_ILN_2111 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 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_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 2019
language	English
source	In Journal of Function Spaces (2019) year:2019
sourceStr	In Journal of Function Spaces (2019) year:2019
format_phy_str_mv	Article
institution	findex.gbv.de
topic_facet	Mathematics
isfreeaccess_bool	true
container_title	Journal of Function Spaces
authorswithroles_txt_mv	Hua Wang @@aut@@
publishDateDaySort_date	2019-01-01T00:00:00Z
hierarchy_top_id	862936489
id	DOAJ046655735
language_de	englisch
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callnumber-first	Q - Science
author	Hua Wang
spellingShingle	Hua Wang misc QA1-939 misc Mathematics Weighted Morrey Spaces Related to Certain Nonnegative Potentials and Riesz Transforms
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topic_title	QA1-939 Weighted Morrey Spaces Related to Certain Nonnegative Potentials and Riesz Transforms
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title	Weighted Morrey Spaces Related to Certain Nonnegative Potentials and Riesz Transforms
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title_full	Weighted Morrey Spaces Related to Certain Nonnegative Potentials and Riesz Transforms
author_sort	Hua Wang
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title_sort	weighted morrey spaces related to certain nonnegative potentials and riesz transforms
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title_auth	Weighted Morrey Spaces Related to Certain Nonnegative Potentials and Riesz Transforms
abstract	Let L=-Δ+V be a Schrödinger operator, where Δ is the Laplacian on Rd and the nonnegative potential V belongs to the reverse Hölder class RHq for q≥d. The Riesz transform associated with the operator L=-Δ+V is denoted by R=∇(-Δ+V)-1/2 and the dual Riesz transform is denoted by R⁎=(-Δ+V)-1/2∇. In this paper, we first introduce some kinds of weighted Morrey spaces related to certain nonnegative potentials belonging to the reverse Hölder class RHq for q≥d. Then we will establish the mapping properties of the operator R and its adjoint R⁎ on these new spaces. Furthermore, the weighted strong-type estimate and weighted endpoint estimate for the corresponding commutators [b,R] and [b,R⁎] are also obtained. The classes of weights, classes of symbol functions, and weighted Morrey spaces discussed in this paper are larger than Ap, BMO(Rd), and Lp,κ(w) corresponding to the classical Riesz transforms (V≡0).
abstractGer	Let L=-Δ+V be a Schrödinger operator, where Δ is the Laplacian on Rd and the nonnegative potential V belongs to the reverse Hölder class RHq for q≥d. The Riesz transform associated with the operator L=-Δ+V is denoted by R=∇(-Δ+V)-1/2 and the dual Riesz transform is denoted by R⁎=(-Δ+V)-1/2∇. In this paper, we first introduce some kinds of weighted Morrey spaces related to certain nonnegative potentials belonging to the reverse Hölder class RHq for q≥d. Then we will establish the mapping properties of the operator R and its adjoint R⁎ on these new spaces. Furthermore, the weighted strong-type estimate and weighted endpoint estimate for the corresponding commutators [b,R] and [b,R⁎] are also obtained. The classes of weights, classes of symbol functions, and weighted Morrey spaces discussed in this paper are larger than Ap, BMO(Rd), and Lp,κ(w) corresponding to the classical Riesz transforms (V≡0).
abstract_unstemmed	Let L=-Δ+V be a Schrödinger operator, where Δ is the Laplacian on Rd and the nonnegative potential V belongs to the reverse Hölder class RHq for q≥d. The Riesz transform associated with the operator L=-Δ+V is denoted by R=∇(-Δ+V)-1/2 and the dual Riesz transform is denoted by R⁎=(-Δ+V)-1/2∇. In this paper, we first introduce some kinds of weighted Morrey spaces related to certain nonnegative potentials belonging to the reverse Hölder class RHq for q≥d. Then we will establish the mapping properties of the operator R and its adjoint R⁎ on these new spaces. Furthermore, the weighted strong-type estimate and weighted endpoint estimate for the corresponding commutators [b,R] and [b,R⁎] are also obtained. The classes of weights, classes of symbol functions, and weighted Morrey spaces discussed in this paper are larger than Ap, BMO(Rd), and Lp,κ(w) corresponding to the classical Riesz transforms (V≡0).
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title_short	Weighted Morrey Spaces Related to Certain Nonnegative Potentials and Riesz Transforms
url	https://doi.org/10.1155/2019/7057512 https://doaj.org/article/1660d5dda7b94d5586d16b23e732be1a http://dx.doi.org/10.1155/2019/7057512 https://doaj.org/toc/2314-8896 https://doaj.org/toc/2314-8888
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up_date	2024-07-03T21:51:58.411Z
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score	7.400075

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Weighted Morrey Spaces Related to Certain Nonnegative Potentials and Riesz Transforms

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