The theta bump condition for product fractional integrals

TL;DR

This paper extends one-parameter fractional integral theorems to a two-parameter setting using a new iteration method, broadening the theoretical understanding of product fractional integrals.

Contribution

It introduces a two-parameter extension of fractional integral theorems employing a recent iteration technique, advancing the theoretical framework.

Findings

Established the theta bump condition for product fractional integrals

Extended Sawyer and Wheeden's theorems to two parameters

Applied Tanaka and Yabuta's iteration method successfully

Abstract

We extend some one parameter theorems on fractional integrals due to Sawyer and Wheeden to the two parameter setting using a recent iteration method of Tanaka and Yabuta.