Geodesic
Characterizations for the Fractional Integral Operators
Matematičeskie zametki, Tome 102 (2017) no. 5, pp. 789-804

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In this paper, we study the boundedness of the fractional integral operator $I_{\alpha}$ on Carnot group $\mathbb{G}$ in the generalized Morrey spaces $M_{p,\varphi}(\mathbb{G})$. 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 $\mathcal{L}$ on $\mathbb{G}$, we prove two Sobolev–Stein embedding theorems on generalized Morrey spaces in the Carnot group setting.
Mots-clés : Carnot group
Keywords: fractional integral operator, generalized Morrey space. 
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     author = {A. Eroglu and V. S. Guliev and J. V. Azizov},
     title = {Characterizations for the {Fractional} {Integral} {Operators}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {789--804},
     publisher = {mathdoc},
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     number = {5},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2017_102_5_a11/}
}
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A. Eroglu; V. S. Guliev; J. V. Azizov. Characterizations for the Fractional Integral Operators. Matematičeskie zametki, Tome 102 (2017) no. 5, pp. 789-804. http://geodesic.mathdoc.fr/item/MZM_2017_102_5_a11/