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


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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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