Karapetyants, A. N.Rafeiro, H.G. Samko, Stefan2020-07-242020-07-242019-110001-4346http://hdl.handle.net/10400.1/14183We 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.engBoundednessLebesgueSingular operatorMorrey spaceBergman-type spaceCalderon-Zygmund operatorjournal article10.1134/S0001434619110075