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On the Generalized Marcinkiewicz Integral Operators with Rough Kernels

Published online by Cambridge University Press:  20 November 2018

Dashan Fan  and
Huoxiong Wu
Dashan Fan
Affiliation:
Department of Mathematics, University of Wisconsin-Milwaukee, Milwaukee, WI, U.S.A. e-mail: fan@csd.uwm.edu
Huoxiong Wu
Affiliation:
School of Mathematical Sciences, Xiamen University, Xiamen Fujian, P. R. China e-mail: huoxwu@xmu.edu.cn
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Abstract

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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

42B2042B2542B3042B99Marcinkiewicz integralLittlewood–Paley theoryTriebel–Lizorkin spacerough kernelproduct domain

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 54 , Issue 1 , 01 March 2011 , pp. 100 - 112
Copyright
Copyright © Canadian Mathematical Society 2011

References

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