Characterization of Riesz and Bessel potentials on variable Lebesgue spaces
Riesz and Bessel potential spaces are studied within the framework of the Lebesgue spaces with variable exponent. It is shown that the spaces of these potentials can be characterized in terms of convergence of hypersingular integrals, if one assumes that the exponent satisfies natural regularity con...
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| Format: | Article |
| Language: | English |
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Wiley
2006-01-01
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| Series: | Journal of Function Spaces and Applications |
| Online Access: | http://dx.doi.org/10.1155/2006/610535 |
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| _version_ | 1832548156599959552 |
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| author | Alexandre Almeida Stefan Samko |
| author_facet | Alexandre Almeida Stefan Samko |
| author_sort | Alexandre Almeida |
| collection | DOAJ |
| description | Riesz and Bessel potential spaces are studied within the framework of the Lebesgue spaces with variable exponent. It is shown that the spaces of these potentials can be characterized in terms of convergence of hypersingular integrals, if one assumes that the exponent satisfies natural regularity conditions. As a consequence of this characterization, we describe a relation between the spaces of Riesz or Bessel potentials and the variable Sobolev spaces. |
| format | Article |
| id | doaj-art-e234ccfd3c8f4777b553c4eeb4d47b83 |
| institution | Kabale University |
| issn | 0972-6802 |
| language | English |
| publishDate | 2006-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces and Applications |
| spelling | doaj-art-e234ccfd3c8f4777b553c4eeb4d47b832025-02-03T06:42:14ZengWileyJournal of Function Spaces and Applications0972-68022006-01-014211314410.1155/2006/610535Characterization of Riesz and Bessel potentials on variable Lebesgue spacesAlexandre Almeida0Stefan Samko1Departamento de Matemática, Universidade de Aveiro, 3810-193 Aveiro, PortugalFaculdade de Ciências e Tecnologia, Universidade do Algarve, Campus de Gambelas, 8005-139 Faro, PortugalRiesz and Bessel potential spaces are studied within the framework of the Lebesgue spaces with variable exponent. It is shown that the spaces of these potentials can be characterized in terms of convergence of hypersingular integrals, if one assumes that the exponent satisfies natural regularity conditions. As a consequence of this characterization, we describe a relation between the spaces of Riesz or Bessel potentials and the variable Sobolev spaces.http://dx.doi.org/10.1155/2006/610535 |
| spellingShingle | Alexandre Almeida Stefan Samko Characterization of Riesz and Bessel potentials on variable Lebesgue spaces Journal of Function Spaces and Applications |
| title | Characterization of Riesz and Bessel potentials on variable Lebesgue spaces |
| title_full | Characterization of Riesz and Bessel potentials on variable Lebesgue spaces |
| title_fullStr | Characterization of Riesz and Bessel potentials on variable Lebesgue spaces |
| title_full_unstemmed | Characterization of Riesz and Bessel potentials on variable Lebesgue spaces |
| title_short | Characterization of Riesz and Bessel potentials on variable Lebesgue spaces |
| title_sort | characterization of riesz and bessel potentials on variable lebesgue spaces |
| url | http://dx.doi.org/10.1155/2006/610535 |
| work_keys_str_mv | AT alexandrealmeida characterizationofrieszandbesselpotentialsonvariablelebesguespaces AT stefansamko characterizationofrieszandbesselpotentialsonvariablelebesguespaces |