Estimates for singular integrals along surfaces of revolution

TL;DR

This paper establishes $L^p$ bounds for non-isotropic singular integrals along surfaces of revolution, providing sharp kernel size conditions for boundedness.

Contribution

It introduces new $L^p$ estimates for singular integrals on surfaces of revolution, advancing understanding of their boundedness properties.

Findings

Proved $L^p$ estimates for non-isotropic singular integrals.

Established $L^p$ boundedness under sharp kernel size conditions.

Enhanced the theoretical framework for singular integrals on surfaces of revolution.

Abstract

We prove certain $L^p$ estimates ($1<p<\infty$) for non-isotropic singular integrals along surfaces of revolution. As an application we obtain $L^p$ boundedness of the singular integrals under a sharp size condition on their kernels.