Convolution on spaces of locally summable functions
In this work we prove the existence of convolution on Marcinkiewicz spaces 𝔐p(ℝ), 1≤p<∞, and, using pointwise approximate identities, we extend the classical definition of Hilbert transform to such spaces.
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2008-01-01
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| Series: | Journal of Function Spaces and Applications |
| Online Access: | http://dx.doi.org/10.1155/2008/817931 |
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| _version_ | 1850218907079540736 |
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| author | Federica Andreano Renato Grande |
| author_facet | Federica Andreano Renato Grande |
| author_sort | Federica Andreano |
| collection | DOAJ |
| description | In this work we prove the existence of convolution on Marcinkiewicz spaces 𝔐p(ℝ), 1≤p<∞, and, using pointwise approximate identities, we extend the classical definition of Hilbert transform to such spaces. |
| format | Article |
| id | doaj-art-7734cd466dbf434ba023738b62b6ca85 |
| institution | OA Journals |
| issn | 0972-6802 |
| language | English |
| publishDate | 2008-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces and Applications |
| spelling | doaj-art-7734cd466dbf434ba023738b62b6ca852025-08-20T02:07:34ZengWileyJournal of Function Spaces and Applications0972-68022008-01-016218720310.1155/2008/817931Convolution on spaces of locally summable functionsFederica Andreano0Renato Grande1Dipartimento di Informatica, Università dell' Insubria, via Mazzini 5, 21100 Varese, ItalyDipartimento di Metodi e Modelli Matematici per le Scienze Applicate, Università di Roma “La Sapienza”, via A. Scarpa 16, 00161 Rome, ItalyIn this work we prove the existence of convolution on Marcinkiewicz spaces 𝔐p(ℝ), 1≤p<∞, and, using pointwise approximate identities, we extend the classical definition of Hilbert transform to such spaces.http://dx.doi.org/10.1155/2008/817931 |
| spellingShingle | Federica Andreano Renato Grande Convolution on spaces of locally summable functions Journal of Function Spaces and Applications |
| title | Convolution on spaces of locally summable functions |
| title_full | Convolution on spaces of locally summable functions |
| title_fullStr | Convolution on spaces of locally summable functions |
| title_full_unstemmed | Convolution on spaces of locally summable functions |
| title_short | Convolution on spaces of locally summable functions |
| title_sort | convolution on spaces of locally summable functions |
| url | http://dx.doi.org/10.1155/2008/817931 |
| work_keys_str_mv | AT federicaandreano convolutiononspacesoflocallysummablefunctions AT renatogrande convolutiononspacesoflocallysummablefunctions |