Fractional integration with singularity on Light-cone,I: natural setting

TL;DR

This paper introduces a new class of fractional integral operators with singularities on the light cone in ^n+1, extending classical results to this novel setting.

Contribution

It proves a Hardy-Littlewood-Sobolev type theorem for fractional integrals with light-cone singularities, a new mathematical framework.

Findings

Established a Hardy-Littlewood-Sobolev inequality for light-cone singular kernels

Extended classical fractional integral theory to light-cone singularities

Provided foundational results for future analysis of light-cone fractional operators

Abstract

In this first part of our project, we prove a classical Hardy-Littlewood-Sobolev result for a new family of fractional integral operators whose kernel has singularity appeared on the light cone in R^n+1.