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.

Saved in:
Bibliographic Details
Main Authors: Federica Andreano, Renato Grande
Format: Article
Language:English
Published: Wiley 2008-01-01
Series:Journal of Function Spaces and Applications
Online Access:http://dx.doi.org/10.1155/2008/817931
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1850218907079540736
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