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Journal of Function Spaces and Applications
Volume 6 (2008), Issue 2, Pages 187-203
http://dx.doi.org/10.1155/2008/817931

Convolution on spaces of locally summable functions

1Dipartimento di Informatica, Università dell' Insubria, via Mazzini 5, 21100 Varese, Italy
2Dipartimento di Metodi e Modelli Matematici per le Scienze Applicate, Università di Roma “La Sapienza”, via A. Scarpa 16, 00161 Rome, Italy

Received 1 July 2006

Academic Editor: Jürgen Appell

Copyright © 2008 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

In this work we prove the existence of convolution on Marcinkiewicz spaces 𝔐p(), 1p<, and, using pointwise approximate identities, we extend the classical definition of Hilbert transform to such spaces.