Generalized Hölder Inequality in Herz-Morrey Spaces with Variable Exponent

Abstract

The paper investigates the conditions for the generalized Hölder’s inequality with a variable exponent in Herz-Morrey spaces. The main results are based on the exponent functions p(·) and α(·) . The proof of the first main result using the generalized Hölder’s inequality in Lebesgue spaces. The second main result of the paper is related to the weak space of the generalized Hölder’s inequality with a variable exponent in Herz-Morrey spaces. The theorems state the equivalence of certain conditions for the inequality. Mathematical proofs and analysis are providing to support the presented results for findings contribute to the understanding of Hölder’s inequalities in variable exponent spaces and their applications in Herz-Morrey spaces.