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Mat. Zametki, 2017, Volume 102, Issue 5, Pages 789–804 (Mi mz11779)  

This article is cited in 3 scientific papers (total in 3 papers)

Characterizations for the Fractional Integral Operators in Generalized Morrey Spaces on Carnot Groups

A. Eroglua, V. S. Gulievbc, J. V. Azizovbd

a Niğde Ömer Halisdemir University
b Institute of Mathematics and Mechanics, Azerbaijan National Academy of Sciences
c Ahi Evran University
d Khazar University

Abstract: 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.

Keywords: Carnot group, fractional integral operator, generalized Morrey space.

Funding Agency Grant Number
Университет им. Ахи Еврана FEF.A3.16.024
Azerbaijan National Academy of Sciences
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).


DOI: https://doi.org/10.4213/mzm11779

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English version:
Mathematical Notes, 2017, 102:5, 722–734

Bibliographic databases:

UDC: 517
Received: 11.04.2017

Citation: A. Eroglu, V. S. Guliev, J. V. Azizov, “Characterizations for the Fractional Integral Operators in Generalized Morrey Spaces on Carnot Groups”, Mat. Zametki, 102:5 (2017), 789–804; Math. Notes, 102:5 (2017), 722–734

Citation in format AMSBIB
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\by A.~Eroglu, V.~S.~Guliev, J.~V.~Azizov
\paper Characterizations for the Fractional Integral Operators
in Generalized Morrey Spaces on Carnot Groups
\jour Mat. Zametki
\yr 2017
\vol 102
\issue 5
\pages 789--804
\mathnet{http://mi.mathnet.ru/mz11779}
\crossref{https://doi.org/10.4213/mzm11779}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3716511}
\elib{http://elibrary.ru/item.asp?id=30512318}
\transl
\jour Math. Notes
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\vol 102
\issue 5
\pages 722--734
\crossref{https://doi.org/10.1134/S0001434617110116}
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\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85039457826}


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    This publication is cited in the following articles:
    1. V. S. Guliyev, A. A. Ahmadli, M. N. Omarova, L. Softova, “Global regularity in Orlicz-Morrey spaces of solutions to nondivergence elliptic equations with VMO coefficients”, Electron. J. Differ. Equ., 2018, 110, 24 pp.  mathscinet  isi
    2. V. S. Guliyev, J. J. Hasanov, X. A. Badalov, “Commutators of Riesz potential in the vanishing generalized weighted Morrey spaces with variable exponent”, Math. Inequal. Appl., 22:1 (2019), 331–351  crossref  mathscinet  isi
    3. Guliyev V., Ekincioglu I., Kaya E., Safarov Z., “Characterizations For the Fractional Maximal Commutator Operator in Generalized Morrey Spaces on Carnot Group”, Integral Transform. Spec. Funct., 30:6 (2019), 453–470  crossref  mathscinet  zmath  isi  scopus
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