Generalized H\"older's inequality on Morrey spaces

TL;DR

This paper establishes necessary and sufficient conditions for generalized H"older's inequality to hold on Morrey and weak Morrey spaces, expanding understanding of inequalities in these function spaces.

Contribution

It provides a complete characterization of when generalized H"older's inequality applies on Morrey and weak Morrey spaces, including necessary and sufficient conditions.

Findings

Characterization of conditions for generalized H"older's inequality on Morrey spaces

Extension of results to weak and generalized weak Morrey spaces

Use of characteristic function estimates in proofs

Abstract

The aim of this paper is to present necessary and sufficient conditions for generalized H\"{o}lder's inequality on generalized Morrey spaces. We also obtain similar results on weak Morrey spaces and on generalized weak Morrey spaces. The necessary and sufficient conditions for the generalized H\"{o}lder's inequality on these spaces are obtained through estimates for characteristic functions of balls in $\mathbb{R}^d$.