Multilinear H\"older-type inequalities on Lorentz sequence spaces

TL;DR

This paper develops H"older-type inequalities for Lorentz sequence spaces and their duals, analyzing diagonal multilinear forms and their norms in various Banach multilinear ideals to extend inequality frameworks.

Contribution

It introduces new H"older-type inequalities specific to Lorentz sequence spaces and explores the norms of multilinear forms in different Banach multilinear ideals, advancing the theoretical understanding.

Findings

Established H"older inequalities for Lorentz sequence spaces

Derived estimates for norms of diagonal multilinear forms

Analyzed multilinear forms in various Banach ideals

Abstract

We establish H\"older type inequalities for Lorentz sequence spaces and their duals. In order to achieve these and some related inequalities, we study diagonal multilinear forms in general sequence spaces, and obtain estimates for their norms. We also consider norms of multilinear forms in different Banach multilinear ideals.