Characterizations for the fractional integral operators in generalized Morrey spaces on Carnot groups

WOS: 000418838500011In this paper, we study the boundedness of the fractional integral operator I (alpha) on Carnot group G in the generalized Morrey spaces M (p, phi) (G). We shall give a characterization for the strong and weak type boundedness of I (alpha) on the generalized Morrey spaces, respectively. As applications of the properties of the fundamental solution of sub-Laplacian L on G, we prove two Sobolev-Stein embedding theorems on generalized Morrey spaces in the Carnot group setting.grant of the Presidium of the Azerbaijan National Academy of ScienceAzerbaijan National Academy of Sciences (ANAS); Ahi Evran University Scientific Research ProjectAhi Evran University [FEF.A3.16.024]The research of V. S. Guliyev was supported in part by the 2015 grant of the Presidium of the Azerbaijan National Academy of Science and by the Ahi Evran University Scientific Research Project under grant FEF.A3.16.024)