Scientific paper “Characterizations For The Fractional Integral Operator And Its Commutators In Generalized Weighted Morrey Spaces On Carnot Groups” by Vagif Guliyev, Professor at the Scientific Research Institute of Applied Mathematics of Baku State University, Corresponding Member of ANAS was published by “Journal of Mathematical Inequalities” (İF: 1.219 (2019)).
In this paper, the authors give a characterization for the strong and weak type Spanne type boundedness of the fractional integral operator Iα , 0 < α < Q on Carnot group G on generalized weighted Morrey spaces Mp,ϕ(G,w), respectively, where Q is the homogeneous dimension of G. They also give a characterization for the Spanne type boundedness of the commutator operator [b,Iα ] on generalized weighted Morrey spaces. As applications of the properties of the fundamental solution of sub-Laplacian L on G, the prove two Sobolev-Stein embedding theorems on generalized weighted Morrey spaces in the Carnot group setting.
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