Extrapolation to two-weighted Herz spaces with three variable exponents

Abstract

On the basis of the boundedness of singular integral operators, we investigate the boundedness of various linear operators acting on two-weighted Herz spaces with three variable exponents. We obtain the extrapolation theorem as well as the boundedness property of bilinear singular operators. First, we are interested in the case where the triangle inequality is available, and then we develop a theory to extend our results in full generality.