Fractional integration with singularity on unit sphere

TL;DR

This paper investigates convolution operators with singular kernels on the unit sphere, establishing L^p-L^q Sobolev inequalities that extend understanding of fractional integration in spherical settings.

Contribution

It introduces a new class of convolution operators with singularities on the sphere and proves associated Sobolev inequalities, advancing fractional integration theory on manifolds.

Findings

Established L^p-L^q Sobolev inequalities for singular convolution operators

Extended fractional integration results to spherical singular kernels

Provided new tools for analysis on the unit sphere

Abstract

We study a family of convolution operators whose kernels have a singularity on the unit sphere. As a result, we prove the regarding L^p-L^q Sobolev inequalities.