Journal of Function Spaces

Journal of Function Spaces / 2010 / Article

Open Access

Volume 8 |Article ID 271905 | 16 pages | https://doi.org/10.1155/2010/271905

Marcinkiewicz integrals with variable kernels on Hardy and weak Hardy spaces

Academic Editor: Maria Carro
Received01 Jul 2007

Abstract

In this article, we consider the Marcinkiewicz integrals with variable kernels defined by μΩ(f)(x)=(0||xy|tΩ(x,xy)|xy|n1f(y)dy|2dtt3)1/2, where Ω(x,z)L(n)×Lq(Sn1) for q > 1. We prove that the operator μΩ is bounded from Hardy space, Hp(n), to Lp(n) space; and is bounded from weak Hardy space, Hp,(n), to weak Lp(n) space for max{2n2n+1,nn+α}<p<1, if Ω satisfies the L1,α-Dini condition with any 0<α1.

Copyright © 2010 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.

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