Maximal Oscillatory Singular Integrals with Kernels in L log L(S^{n-1})

Authors: AHMAD AL-SALMAN

Abstract: In this paper, we study the L^p mapping properties of a certain class of maximal oscillatory singular integral operators. We establish the L^p boundedness of our operators provided that their kernels belong to the natural space L log ^+L(S^{n-1}). Our result substantially improves a previously known result. Moreover, the approach developed in this paper can be applied to handle more general maximal oscillatory singular integral operators.

Keywords: Oscillatory singular integrals, Rough kernels, Maximal functions

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