Some applications of the H\"older inequality for mixed sums

TL;DR

This paper applies the H"older inequality for mixed exponents to establish optimal variants of the generalized Hardy--Littlewood inequality for m-linear forms on b5 spaces with mixed exponents, extending recent research.

Contribution

It introduces new optimal variants of the Hardy--Littlewood inequality for m-linear forms using mixed exponent H"older inequality, advancing the theoretical understanding.

Findings

Derived optimal inequalities for m-linear forms

Extended previous results to broader b5 space settings

Enhanced the theoretical framework for mixed sums inequalities

Abstract

We use the H\"{o}lder inequality for mixed exponents to prove some optimal variants of the generalized Hardy--Littlewood inequality for $m$-linear forms on $\ell _{p}$ spaces with mixed exponents. Our results extend recent results of Araujo et al.