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On maximal functions with rough kernels in L (log L)(S).

Ahmad Al-Salman — 2005

Collectanea Mathematica

In this paper, we study the L mapping properties of maximal functions with rough kernels that are related to certain class of singular integral operators. We prove that our maximal functions are bounded on L provided that their kernels are in L (log L)(S). Moreover, we present an example showing that our size condition on the kernel is optimal. As a consequence of our result, we substantially improve previously known results on maximal functions, singular integral operators, and Parametric Marcinkiewicz...

Rough Maximal Oscillatory Singular Integral Operators

Al-Salman, Ahmad — 2005

Fractional Calculus and Applied Analysis

2000 Mathematics Subject Classification: Primary 42B20; Secondary 42B15, 42B25 In this paper, we establish the L^p boundedness of certain maximal oscillatory singular integral operators with rough kernels belonging to certain block spaces. Our L^p boundedness result improves previously known results.

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