An extension of the Muckenhoupt-Wheeden theorem to generalized weighted Morrey spaces

Abstract

In this paper, we find the condition on a function ? and a weight v which ensures the equivalency of norms of the Riesz potential and the fractional maximal function in generalized weighted Morrey spaces Mp,?(Rn , v) and generalized weighted central Morrey spaces ˙M p,?(Rn , v), when v belongs to the Muckenhoupt A?-class. © 2020 Walter de Gruyter GmbH, Berlin/Boston 2020.