# New Young inequalities and applications

## TL;DR

This paper develops new Young inequalities for convolution operators in interpolation spaces, providing bounds, a bilinear interpolation theorem, and applications to bilinear multipliers in various function spaces.

## Contribution

It introduces novel Young inequalities in the context of interpolation spaces and applies them to bilinear interpolation and multiplier problems.

## Key findings

- Established new upper bounds for convolution operators.
- Proved a bilinear interpolation theorem.
- Applied results to bilinear multiplier analysis.

## Abstract

We establish upper bounds for the convolution operator acting between interpolation spaces. This will provide several examples of Young Inequalities in different families of function spaces. We use this result to prove a bilinear interpolation theorem and we show applications to the study of bilinear multipliers.