Characterizations for the fractional maximal operator and its commutators in generalized weighted Morrey spaces on Carnot groups

Abstract

In this paper, we shall give a characterization for the strong and weak type Spanne type boundedness of the fractional maximal operator $$M_{\alpha }$$ , $$0\le \alpha <Q$$ on Carnot group $${{\mathbb {G}}}$$ on generalized weighted Morrey spaces $$M_{p,\varphi }({{\mathbb {G}}},w)$$ , where Q is the homogeneous dimension of $${{\mathbb {G}}}$$ . Also we give a characterization for the Spanne type boundedness of the fractional maximal commutator operator $$M_{b,\alpha }$$ on generalized weighted Morrey spaces.