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Georgian Mathematical Journal

Editor-in-Chief: Kiguradze, Ivan / Buchukuri, T.

Editorial Board: Kvinikadze, M. / Bantsuri, R. / Baues, Hans-Joachim / Besov, O.V. / Bojarski, B. / Duduchava, R. / Engelbert, Hans-Jürgen / Gamkrelidze, R. / Gubeladze, J. / Hirzebruch, F. / Inassaridze, Hvedri / Jibladze, M. / Kadeishvili, T. / Kegel, Otto H. / Kharazishvili, Alexander / Kharibegashvili, S. / Khmaladze, E. / Kiguradze, Tariel / Kokilashvili, V. / Krushkal, S. I. / Kurzweil, J. / Kwapien, S. / Lerche, Hans Rudolf / Mawhin, Jean / Ricci, P.E. / Tarieladze, V. / Triebel, Hans / Vakhania, N. / Zanolin, Fabio


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1572-9176
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Variable exponent fractional integrals in the limiting case α(x)p(n) ≡ n on quasimetric measure spaces

Stefan Samko
  • Corresponding author
  • Departamento de Matemática, Faculdade de Ciências e Tecnologia, Universidade do Algarve, Faro, Portugal
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Published Online: 2018-07-18 | DOI: https://doi.org/10.1515/gmj-2018-0047

Abstract

We show that the fractional operator Iα(), of variable order on a bounded open set in Ω, in a quasimetric measure space (X,d,μ) in the case α(x)p(x)n (where n comes from the growth condition on the measure μ), is bounded from the variable exponent Lebesgue space Lp()(Ω) into BMO(Ω) under certain assumptions on p(x) and α(x).

Keywords: Riesz potential; variable exponent spaces; Sobolev type theorem; BMO results,quasimetric measure space

MSC 2010: 46E30

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About the article

Received: 2016-01-23

Accepted: 2016-06-03

Published Online: 2018-07-18


The research was supported by grant No. 15-01-02732 of Russian Fund of Basic Research.


Citation Information: Georgian Mathematical Journal, ISSN (Online) 1572-9176, ISSN (Print) 1072-947X, DOI: https://doi.org/10.1515/gmj-2018-0047.

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