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On a Class of Singular Integral Operators With Rough Kernels

  Published:2006-03-01
 Printed: Mar 2006
  • Ahmad Al-Salman
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Abstract

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 Calder\'{o}n--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: Singular integrals, Rough kernels, Square functions, Maximal functions, Block spaces Singular integrals, Rough kernels, Square functions, Maximal functions, Block spaces
MSC Classifications: 42B20, 42B15, 42B25 show english descriptions Singular and oscillatory integrals (Calderon-Zygmund, etc.)
Multipliers
Maximal functions, Littlewood-Paley theory
42B20 - Singular and oscillatory integrals (Calderon-Zygmund, etc.)
42B15 - Multipliers
42B25 - Maximal functions, Littlewood-Paley theory
 

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