An extension of Muchenhoupt-Wheeden theorem to generalized weighted (central) Morrey spaces

In this paper we find the condition on function $\omega$ and weight $v$ which ensures the equivalency of norms of the Riesz potential and the fractional maximal function in generalized weighted Morrey spaces ${\mathcal M}{p,\omega}({\mathbb R}^n,v)$andgeneralizedweightedcentralMorreyspaces$\dot{\mathcal M}{p,\omega}({\mathbb R}^n,v)$,when$v$belongstoMuckenhoupt$A_{\infty}$-class.