On Singular Operators in Vanishing Generalized Variable-Exponent Morrey Spaces and Applications to Bergman-Type Spaces
- Authors: Karapetyants A.N.1,2, Rafeiro H.3, Samko S.G.4
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Affiliations:
- Southern Federal University
- State University of New York
- Department of Mathematical Sciences, College of Sciences
- University of Algarve
- Issue: Vol 106, No 5-6 (2019)
- Pages: 727-739
- Section: Article
- URL: https://journal-vniispk.ru/0001-4346/article/view/151853
- DOI: https://doi.org/10.1134/S0001434619110075
- ID: 151853
Cite item
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 Rn, 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.
About the authors
A. N. Karapetyants
Southern Federal University; State University of New York
Author for correspondence.
Email: karapetyants@gmail.com
Russian Federation, Rostov-on-Don, 334006; Albany, 12222
H. Rafeiro
Department of Mathematical Sciences, College of Sciences
Author for correspondence.
Email: rafeiro@uaeu.ac.ae
United Arab Emirates, Al Ain, 15551
S. G. Samko
University of Algarve
Author for correspondence.
Email: ssamko@ualg.pt
Portugal, Faro, 8005-139
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