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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


IMPACT FACTOR 2018: 0.551

CiteScore 2018: 0.52

SCImago Journal Rank (SJR) 2018: 0.320
Source Normalized Impact per Paper (SNIP) 2018: 0.711

Mathematical Citation Quotient (MCQ) 2017: 0.23

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1572-9176
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L p(·)L q(·) boundedness of some integral operators obtained by extrapolation techniques

Marta Urciuolo / Lucas Vallejos
Published Online: 2018-11-14 | DOI: https://doi.org/10.1515/gmj-2018-0066

Abstract

Given a matrix A such that AM=I and 0α<n, for an exponent p satisfying p(Ax)=p(x) for a.e. xn, using extrapolation techniques, we obtain Lp()Lq() boundedness, 1q()=1p()-αn, and weak type estimates for integral operators of the form

Tαf(x)=f(y)|x-A1y|α1|x-Amy|αm𝑑y,

where A1,,Am are different powers of A such that Ai-Aj is invertible for ij, α1++αm=n-α. We give some generalizations of these results.

Keywords: Variable exponents; fractional integrals

MSC 2010: 42B25; 42B35

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About the article

Received: 2016-10-10

Revised: 2017-01-27

Accepted: 2017-08-24

Published Online: 2018-11-14


Partially supported by CONICET and SECYTUNC.


Citation Information: Georgian Mathematical Journal, ISSN (Online) 1572-9176, ISSN (Print) 1072-947X, DOI: https://doi.org/10.1515/gmj-2018-0066.

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