Estimates for singular integrals along surfaces of revolution

概要

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We prove certain Lp estimates (1<p<) for nonisotropic singular integrals along surfaces of revolution. The singular integrals are defined by rough kernels. As an application we obtain Lp boundedness of the singular integrals under a sharp size condition on their kernels. We also prove a certain estimate for a trigonometric integral, which is useful in studying nonisotropic singular integrals. © 2009 Copyright Australian Mathematical Society.