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# On the Generalized Marcinkiewicz Integral Operators with Rough Kernels

Published:2010-08-03
Printed: Mar 2011
• Dashan Fan,
Department of Mathematics, University of Wisconsin-Milwaukee, Milwaukee, WI, U.S.A.
• Huoxiong Wu,
School of Mathematical Sciences, Xiamen University, Xiamen Fujian, P.~R. China
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## Abstract

A class of generalized Marcinkiewicz integral operators is introduced, and, under rather weak conditions on the integral kernels, the boundedness of such operators on $L^p$ and Triebel--Lizorkin spaces is established.
 Keywords: Marcinkiewicz integral, Littlewood--Paley theory, Triebel--Lizorkin space, rough kernel, product domain
 MSC Classifications: 42B20 - Singular and oscillatory integrals (Calderon-Zygmund, etc.) 42B25 - Maximal functions, Littlewood-Paley theory 42B30 - $H^p$-spaces 42B99 - None of the above, but in this section

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