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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Dedicated to Professor Stefan Samko on the occasion of his 75th birthday.
Original Russian Text © A. Eroglu, V. S. Guliyev, J. V. Azizov, 2017, published in Matematicheskie Zametki, 2017, Vol. 102, No. 5, pp. 789–804.
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Eroglu, A., Guliyev, V.S. & Azizov, J.V. Characterizations for the fractional integral operators in generalized Morrey spaces on Carnot groups. Math Notes 102, 722–734 (2017). https://doi.org/10.1134/S0001434617110116