Extrapolation to Morrey Banach spaces on spaces of homogeneous type

Abstract

This paper introduces the Morrey Banach spaces on spaces of homogeneous type. We establish the Rubio de Francia extrapolation theory for Morrey Banach spaces on spaces of homogeneous type. Consequently, we obtain the boundedness of the Calderón–Zygmund operators and the Fefferman–Stein inequalities on Morrey Banach spaces on spaces of homogeneous type. We apply the results obtained for Morrey Banach space to study the Morrey spaces with variable exponents on spaces of homogeneous type.