L^p Boundedness of a Class of Singular Integral Operators with Rough Kernels

Authors: AHMAD AL-SALMAN, HUSSAIN AL-QUASSEM

Abstract: In this paper, we study the L^p mapping properties of singular integral operators with kernels belonging to certain block spaces. These operators have singularities along sets of the form {x=\Phi (|y|)y^'} where \Phi satisfies certain growth conditions. Our results improve as well as extend previously known results on singular integrals.

Keywords: Singular integrals, oscillatory integrals, Fourier transform, L^p boundedness, rough kernels, block spaces.

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