# Anisotropic Regularity Principle in sequence spaces and applications

## TL;DR

This paper introduces a generalized anisotropic regularity principle in sequence spaces, extending existing results and applying it to improve Hardy--Littlewood inequalities for multilinear forms.

## Contribution

It refines a recent technique to establish a broad anisotropic regularity principle and generalizes previous Hardy--Littlewood inequality results for multilinear forms.

## Key findings

- Established a general anisotropic regularity principle in sequence spaces.
- Extended Hardy--Littlewood inequalities for multilinear forms.
- Unified and improved previous results in the literature.

## Abstract

We refine a recent technique introduced by Pellegrino, Santos, Serrano and Teixeira and prove a quite general anisotropic regularity principle in sequence spaces. As applications we generalize previous results of several authors regarding Hardy--Littlewood inequalities for multilinear forms.