Singular integrals and potentials in some Banach function spaces with variable exponent
We introduce a new Banach function space - a Lorentz type space with variable exponent. In this space the boundedness of singular integral and potential type operators is established, including the weighted case. The variable exponent p(t) is assumed to satisfy the logarithmic Dini condition and the...
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| Format: | Article |
| Language: | English |
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Wiley
2003-01-01
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| Series: | Journal of Function Spaces and Applications |
| Online Access: | http://dx.doi.org/10.1155/2003/932158 |
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| _version_ | 1832554401764474880 |
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| author | Vakhtang Kokilashvili Stefan Samko |
| author_facet | Vakhtang Kokilashvili Stefan Samko |
| author_sort | Vakhtang Kokilashvili |
| collection | DOAJ |
| description | We introduce a new Banach function space - a Lorentz type space with variable exponent. In this space the boundedness of singular integral and potential type operators is established, including the weighted case. The variable exponent p(t) is assumed to satisfy the logarithmic Dini condition and the exponent β of the power weight ω(t)=|t|β is related only to the value p(0). The mapping properties of Cauchy singular integrals defined on Lyapunov curves and on curves of bounded rotation are also investigated within the framework of the introduced spaces. |
| format | Article |
| id | doaj-art-f9c828c708664068961c587baf34b3c9 |
| institution | Kabale University |
| issn | 0972-6802 |
| language | English |
| publishDate | 2003-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces and Applications |
| spelling | doaj-art-f9c828c708664068961c587baf34b3c92025-02-03T05:51:40ZengWileyJournal of Function Spaces and Applications0972-68022003-01-0111455910.1155/2003/932158Singular integrals and potentials in some Banach function spaces with variable exponentVakhtang Kokilashvili0Stefan Samko1A. Razmadze Mathematical Institute, M. Aleksidze St., 1, 380093 Tbilisi, GeorgiaUniversidade do Algarve, Faro 8000, PortugalWe introduce a new Banach function space - a Lorentz type space with variable exponent. In this space the boundedness of singular integral and potential type operators is established, including the weighted case. The variable exponent p(t) is assumed to satisfy the logarithmic Dini condition and the exponent β of the power weight ω(t)=|t|β is related only to the value p(0). The mapping properties of Cauchy singular integrals defined on Lyapunov curves and on curves of bounded rotation are also investigated within the framework of the introduced spaces.http://dx.doi.org/10.1155/2003/932158 |
| spellingShingle | Vakhtang Kokilashvili Stefan Samko Singular integrals and potentials in some Banach function spaces with variable exponent Journal of Function Spaces and Applications |
| title | Singular integrals and potentials in some Banach function spaces with variable exponent |
| title_full | Singular integrals and potentials in some Banach function spaces with variable exponent |
| title_fullStr | Singular integrals and potentials in some Banach function spaces with variable exponent |
| title_full_unstemmed | Singular integrals and potentials in some Banach function spaces with variable exponent |
| title_short | Singular integrals and potentials in some Banach function spaces with variable exponent |
| title_sort | singular integrals and potentials in some banach function spaces with variable exponent |
| url | http://dx.doi.org/10.1155/2003/932158 |
| work_keys_str_mv | AT vakhtangkokilashvili singularintegralsandpotentialsinsomebanachfunctionspaceswithvariableexponent AT stefansamko singularintegralsandpotentialsinsomebanachfunctionspaceswithvariableexponent |