A two-parameter Hedberg's method for fractional integration

TL;DR

This paper introduces a novel two-parameter Hedberg's method to establish a Hardy-Littlewood-Sobolev theorem for fractional integral operators with kernels singular on the light-cone, expanding the theoretical framework of fractional integration.

Contribution

The paper develops a new two-parameter Hedberg's method and applies it to prove a Hardy-Littlewood-Sobolev theorem for a novel class of fractional integral operators with light-cone singularities.

Findings

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

Introduced a two-parameter Hedberg's method for fractional integration

Extended fractional integral theory to new kernel types

Abstract

We introduce a 2-parameter Hedberg's method, and use it to prove a Hardy-Littlewood-Sobolev theorem for a new type of fractional integral operators, whose kernel has singularity on the light-cone.