# Bilinear estimates on Morrey spaces by using average

## TL;DR

This paper studies the boundedness of bilinear fractional integral operators on Morrey spaces, focusing on the case where the parameter t is between 0 and 1, extending previous results to this range.

## Contribution

It extends the analysis of bilinear fractional integral operators on Morrey spaces to include the case where 0<t<1, filling a gap in existing research.

## Key findings

- Established boundedness results for 0<t<1 on Morrey spaces.
- Extended previous work that covered t=1 and t>1.
- Provided new estimates for bilinear fractional integral operators.

## Abstract

This paper is a follow up of [6]. We investigate the boundedness of the bilinear fractional integral operator introduced by Grafakos in [3]. When the local integrability index $s$ falls 1 with weights and $t$ exceeds 1, He and Yan obtained some results on this operator was worked on Morrey spaces earlier in [7]. Later in the paper [6], we considered the case $t=1$. This paper handles the remaining case $0<t<1$.