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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 Marcinkiewicz integral, Littlewood--Paley theory, Triebel--Lizorkin space, rough kernel, product domain
MSC Classifications: 42B20, 42B25, 42B30, 42B99 show english descriptions Singular and oscillatory integrals (Calderon-Zygmund, etc.)
Maximal functions, Littlewood-Paley theory
$H^p$-spaces
None of the above, but in this section
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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