# Regularized Brascamp-Lieb inequalities and an application

## TL;DR

This paper introduces a regularized form of the Brascamp-Lieb inequalities, extending their applicability and leading to a generalized multilinear Kakeya inequality, with implications for harmonic analysis.

## Contribution

It proposes a novel regularization of the Brascamp-Lieb inequalities and demonstrates their application to a broader multilinear Kakeya inequality.

## Key findings

- Regularized Brascamp-Lieb inequalities established.
- Generalized multilinear Kakeya inequality derived.
- Potential applications in harmonic analysis explored.

## Abstract

We present a regularized version of H\"{o}lder-Brascamp-Lieb inequalities studied by Bennett, Carbery, Christ, and Tao. These inequalities lead to a generalization of the multilinear Kakeya inequality.