The rectangular fractional integral operators

TL;DR

This paper establishes a generalized Hardy-Littlewood-Sobolev inequality for rectangular fractional integral operators using rectangular doubling weights and dyadic rectangles, expanding the theoretical understanding of these operators.

Contribution

It introduces a new inequality for rectangular fractional integrals based on rectangular doubling weights, utilizing an $M$-linear embedding theorem for dyadic rectangles.

Findings

Proves a generalized Hardy-Littlewood-Sobolev inequality for rectangular fractional integrals.

Applies $M$-linear embedding theorem to dyadic rectangles in the proof.

Enhances theoretical framework for fractional integral operators in rectangular settings.

Abstract

With rectangular doubling weight, a~generalized Hardy-Littlewood-Sobolev inequality for rectangular fractional integral operators is verified. The result is a~nice application of $M$-linear embedding theorem for dyadic rectangles.