On singular operators in vanishing generalized variable-exponent Morrey spaces and applications to Bergman-type spaces

Karapetyants, A. N.; Rafeiro, H.; G. Samko, Stefan

http://hdl.handle.net/10400.1/14183

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Authors

Karapetyants, A. N.

Rafeiro, H.

G. Samko, Stefan

Abstract(s)

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 Calderon-Zygmund operators on generalized variable-exponent vanishing Morrey spaces. We give the proof of the latter in the general context of real functions on 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.