On Some Properties of Integral-Type Operator in Weighted Herz Spaces with Variable Exponent Lebesgue Spaces

Abstract

For the last quarter century a considerable number of research has been carried out on the study of Herz spaces, variable exponent Lebesgue spaces and Sobolev spaces. This studies also have played an important role in problems of elasticity, fluid dynamics, calculus of variations. Our aim in this work is to prove some properties of the integral-type operator on weighted Herz space with variable exponent Lebesgue space (VELS).