Generalized H(?)lder’s Inequality In Weighted Spaces And Property Of Variable Block Spaces

This paper is devoted to studying the generalized Holder inequality of weighted space under the background of n-dimensional Euclidean space and the properties of variable index Block space under the background of metric space.Holder inequality is one of the classic inequalities,in harmony Analysis,functional analysis and other disciplines play an important role.On the other hand,the variable index function space is not only widely used in the research of harmonic analysis and partial differential equations,but also has very important applications in practical problems such as fluid mechanics,image processing,and variational problems.This paper proves the necessary and sufficient conditions of the generalized Holder inequality on the weighted weak Lebesgue space and the special weighted Morrey space(see Theorem 2.3.6 and 2.4.7),establishes the equivalent characterization of the variable index Mp(·)u(χ)in the context of the measurement space,proves the Holder inequality between Morrey space Mp(·)u(X)and Block space Bu,p(·)(X),and uses the Hahn-Banach theorem to prove the dual space of Bu,p(·)(χ)is Mp’(·)u(χ).