Maximal Oscillatory Singular Integrals with Kernels in L log L(Sn-1)

In this paper, we study the Lp mapping properties of a certain class of maximal oscillatory singular integral operators. We establish the Lp boundedness of our operators provided that their kernels belong to the natural space L log +L(Sn-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.

Anahtar Kelimeler:

Oscillatory singular integrals, Rough kernels, Maximal functions

Maximal Oscillatory Singular Integrals with Kernels in L log L(Sn-1)

Keywords:

Oscillatory singular integrals, Rough kernels, Maximal functions,

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Department of Mathematics Yarmouk University Irbid-JORDAN e-mail: alsalman@yu.edu.jo