Characterizations for the fractional integral operators in generalized Morrey spaces on Carnot groups |
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| Authors: | A Eroglu V S Guliyev J V Azizov |
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| Institution: | 1.Ni?de ?mer Halisdemir University,Ni?de,Turkey;2.Ahi Evran University,Kirsehir,Turkey;3.Institute of Mathematics and Mechanics,National Academy of Sciences of Azerbaijan,Baku,Azerbaijan;4.Khazar University,Baku,Azerbaijan |
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| Abstract: | In this paper, we study the boundedness of the fractional integral operator I α on Carnot group G in the generalized Morrey spaces M p, φ (G). We shall give a characterization for the strong and weak type boundedness of I α 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. |
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