Lp-Boundedness of general index transforms
Abstract We establish the boundedness properties in Lp for a class of integral transformations with respect to an index of hypergeometric functions. In particular, by using the Riesz-Thorin interpolation theorem, we get the corresponding results in Lp(R+), 1 ⩽ p ⩽ 2, for the Kontorovich-Lebedev, Meh...
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Gespeichert in:
| Autor*in: |
Yakubovich, S. B. [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2005 |
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| Schlagwörter: |
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| Anmerkung: |
© Springer Science+Business Media, Inc. 2005 |
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| Übergeordnetes Werk: |
Enthalten in: Lithuanian mathematical journal - Kluwer Academic Publishers-Consultants Bureau, 1975, 45(2005), 1 vom: Jan., Seite 102-122 |
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| Übergeordnetes Werk: |
volume:45 ; year:2005 ; number:1 ; month:01 ; pages:102-122 |
| Links: |
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| DOI / URN: |
10.1007/s10986-005-0011-x |
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OLC2069935116 |
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| 520 | |a Abstract We establish the boundedness properties in Lp for a class of integral transformations with respect to an index of hypergeometric functions. In particular, by using the Riesz-Thorin interpolation theorem, we get the corresponding results in Lp(R+), 1 ⩽ p ⩽ 2, for the Kontorovich-Lebedev, Mehler-Fock, and Olevskii index transforms. An inversion theorem is proved for a general index transformation. The case p=2 is known as the Plancherel-type theory for this class of transformations. | ||
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| 650 | 4 | |a Hausdorff-Young inequality | |
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| 650 | 4 | |a Mellin transform | |
| 650 | 4 | |a Mehler-Fock transform | |
| 650 | 4 | |a Olevskii transform | |
| 650 | 4 | |a Plancherel theory | |
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10.1007/s10986-005-0011-x doi (DE-627)OLC2069935116 (DE-He213)s10986-005-0011-x-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn Yakubovich, S. B. verfasserin aut Lp-Boundedness of general index transforms 2005 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media, Inc. 2005 Abstract We establish the boundedness properties in Lp for a class of integral transformations with respect to an index of hypergeometric functions. In particular, by using the Riesz-Thorin interpolation theorem, we get the corresponding results in Lp(R+), 1 ⩽ p ⩽ 2, for the Kontorovich-Lebedev, Mehler-Fock, and Olevskii index transforms. An inversion theorem is proved for a general index transformation. The case p=2 is known as the Plancherel-type theory for this class of transformations. Kontorovich-Lebedev transform Hausdorff-Young inequality Fourier transform Mellin transform Mehler-Fock transform Olevskii transform Plancherel theory Enthalten in Lithuanian mathematical journal Kluwer Academic Publishers-Consultants Bureau, 1975 45(2005), 1 vom: Jan., Seite 102-122 (DE-627)130618624 (DE-600)795211-9 (DE-576)016125312 0363-1672 nnns volume:45 year:2005 number:1 month:01 pages:102-122 https://doi.org/10.1007/s10986-005-0011-x lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_40 GBV_ILN_70 AR 45 2005 1 01 102-122 |
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10.1007/s10986-005-0011-x doi (DE-627)OLC2069935116 (DE-He213)s10986-005-0011-x-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn Yakubovich, S. B. verfasserin aut Lp-Boundedness of general index transforms 2005 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media, Inc. 2005 Abstract We establish the boundedness properties in Lp for a class of integral transformations with respect to an index of hypergeometric functions. In particular, by using the Riesz-Thorin interpolation theorem, we get the corresponding results in Lp(R+), 1 ⩽ p ⩽ 2, for the Kontorovich-Lebedev, Mehler-Fock, and Olevskii index transforms. An inversion theorem is proved for a general index transformation. The case p=2 is known as the Plancherel-type theory for this class of transformations. Kontorovich-Lebedev transform Hausdorff-Young inequality Fourier transform Mellin transform Mehler-Fock transform Olevskii transform Plancherel theory Enthalten in Lithuanian mathematical journal Kluwer Academic Publishers-Consultants Bureau, 1975 45(2005), 1 vom: Jan., Seite 102-122 (DE-627)130618624 (DE-600)795211-9 (DE-576)016125312 0363-1672 nnns volume:45 year:2005 number:1 month:01 pages:102-122 https://doi.org/10.1007/s10986-005-0011-x lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_40 GBV_ILN_70 AR 45 2005 1 01 102-122 |
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Abstract We establish the boundedness properties in Lp for a class of integral transformations with respect to an index of hypergeometric functions. In particular, by using the Riesz-Thorin interpolation theorem, we get the corresponding results in Lp(R+), 1 ⩽ p ⩽ 2, for the Kontorovich-Lebedev, Mehler-Fock, and Olevskii index transforms. An inversion theorem is proved for a general index transformation. The case p=2 is known as the Plancherel-type theory for this class of transformations. © Springer Science+Business Media, Inc. 2005 |
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Abstract We establish the boundedness properties in Lp for a class of integral transformations with respect to an index of hypergeometric functions. In particular, by using the Riesz-Thorin interpolation theorem, we get the corresponding results in Lp(R+), 1 ⩽ p ⩽ 2, for the Kontorovich-Lebedev, Mehler-Fock, and Olevskii index transforms. An inversion theorem is proved for a general index transformation. The case p=2 is known as the Plancherel-type theory for this class of transformations. © Springer Science+Business Media, Inc. 2005 |
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Abstract We establish the boundedness properties in Lp for a class of integral transformations with respect to an index of hypergeometric functions. In particular, by using the Riesz-Thorin interpolation theorem, we get the corresponding results in Lp(R+), 1 ⩽ p ⩽ 2, for the Kontorovich-Lebedev, Mehler-Fock, and Olevskii index transforms. An inversion theorem is proved for a general index transformation. The case p=2 is known as the Plancherel-type theory for this class of transformations. © Springer Science+Business Media, Inc. 2005 |
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B.</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Lp-Boundedness of general index transforms</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2005</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">ohne Hilfsmittel zu benutzen</subfield><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Band</subfield><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">© Springer Science+Business Media, Inc. 2005</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract We establish the boundedness properties in Lp for a class of integral transformations with respect to an index of hypergeometric functions. In particular, by using the Riesz-Thorin interpolation theorem, we get the corresponding results in Lp(R+), 1 ⩽ p ⩽ 2, for the Kontorovich-Lebedev, Mehler-Fock, and Olevskii index transforms. An inversion theorem is proved for a general index transformation. 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