Generalized Hölder's inequality on Morrey spaces

Abstract

The aim of this paper is to present necessary and sufficient conditions for generalized Hölder'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 Hölder's inequality on these spaces are obtained through estimates for characteristic functions of balls in $\mathbb{R}^d$.