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On a Class of Singular Integral Operators With Rough Kernels

Published online by Cambridge University Press:  20 November 2018

Ahmad Al-Salman
Ahmad Al-Salman*
Affiliation:
Department of Mathematics, Yarmouk University, Irbid, Jordan email: alsalman@yu.edu.jo
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Abstract

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In this paper, we study the ${{L}^{p}}$ mapping properties of a class of singular integral operators with rough kernels belonging to certain block spaces. We prove that our operators are bounded on ${{L}^{p}}$ provided that their kernels satisfy a size condition much weaker than that for the classical Calderón–Zygmund singular integral operators. Moreover, we present an example showing that our size condition is optimal. As a consequence of our results, we substantially improve a previously known result on certain maximal functions.

Keywords

42B2042B1542B25Singular integralsRough kernelsSquare functionsMaximal functionsBlock spaces

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 49 , Issue 1 , 01 March 2006, pp. 3 - 10
Copyright
Copyright © Canadian Mathematical Society 2006

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