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

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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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Authors and Affiliations

  1. Niğde Ömer Halisdemir University, Niğde, Turkey

    A. Eroglu

  2. Ahi Evran University, Kirsehir, Turkey

    V. S. Guliyev

  3. Institute of Mathematics and Mechanics, National Academy of Sciences of Azerbaijan, Baku, Azerbaijan

    V. S. Guliyev & J. V. Azizov

  4. Khazar University, Baku, Azerbaijan

    J. V. Azizov

Authors
  1. A. Eroglu
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  2. V. S. Guliyev
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  3. J. V. Azizov
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Correspondence to A. Eroglu.

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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

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