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Mat. Zametki, 2019, Volume 106, Issue 5, paper published in the English version journal (Mi mz12188)  

Papers published in the English version of the journal

On Singular Operators in Vanishing Generalized Variable-Exponent Morrey Spaces and Applications to Bergman-Type Spaces

A. N. Karapetyantsab, H. Rafeiroc, S. G. Samkod

a Southern Federal University, Rostov-on-Don, 334006 Russia
b State University of New York at Albany, 12222 USA
c Department of Mathematical Sciences, College of Sciences, United Arab Emirates University, Al Ain, 15551 UAE
d University of Algarve, Faro, 8005-139 Portugal

Abstract: We give a proof of the boundedness of the Bergman projection in generalized variable-exponent vanishing Morrey spaces over the unit disc and the upper half-plane. To this end, we prove the boundedness of the Calderón–Zygmund operators on generalized variable-exponent vanishing Morrey spaces. We give the proof of the latter in the general context of real functions on $\mathbb R^n$, since it is new in such a setting and is of independent interest. We also study the approximation by mollified dilations and estimate the growth of functions near the boundary.

Keywords: singular operator, Morrey space, Bergman-type space, Calderón–Zygmund operator.

Funding Agency Grant Number
Russian Foundation for Basic Research 18-01-00094
18-51-05009 Arm-a
19-01-00223
United Arab Emirates University G00002994
The work of A. N. Karapetyants and S. G. Samko was supported in part by the Russian Foundation for Basic Research under grant 18-01-00094. The work of A. N. Karapetyants was also supported in part by the Russian Foundation for Basic Research under grant 18-51-05009 Arm-a and by Visiting Fulbright Scholar Program. The research of H. Rafeiro was supported by a Research Start-up Grant of United Arab Emirates University, Al Ain, United Arab Emirates, via grant no. G00002994. The research of S. Samko was supported by the Russian Foundation for Basic Research under grant 19-01-00223.

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English version:
Mathematical Notes, 2019, 106:5, 727–739

Bibliographic databases:

Received: 13.09.2018
Revised: 16.02.2019
Language:

Citation: A. N. Karapetyants, H. Rafeiro, S. G. Samko, “On Singular Operators in Vanishing Generalized Variable-Exponent Morrey Spaces and Applications to Bergman-Type Spaces”, Math. Notes, 106:5 (2019), 727–739

Citation in format AMSBIB
\Bibitem{KarRafSam19}
\by A.~N.~Karapetyants, H.~Rafeiro, S.~G.~Samko
\paper On Singular Operators in Vanishing Generalized Variable-Exponent
Morrey Spaces and Applications to Bergman-Type Spaces
\jour Math. Notes
\yr 2019
\vol 106
\issue 5
\pages 727--739
\mathnet{http://mi.mathnet.ru/mz12188}
\crossref{https://doi.org/10.1134/S0001434619110075}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000504614300007}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85077091321}


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