It is shown that on strongly pseudoconvex domains the Bergman projection maps a space of functions growing near the boundary like some power of the Bergman distance from a fixed point into a space of functions which can be estimated by the consecutive power of the Bergman distance. This property has a local character. Let Ω be a bounded, pseudoconvex set with C³ boundary. We show that if the Bergman projection is continuous on a space defined by weighted-sup seminorms and equipped with the topology given by these seminorms, then E must contain the spaces for each natural k. As a result, in the case of strongly pseudoconvex domains the inductive limit of this sequence of spaces is the smallest extension of in the class of spaces defined by weighted-sup seminorms on which the Bergman projection is continuous. This is a generalization of the results of J. Taskinen in the case of the unit disc as well as of the previous research of the author concerning the unit ball.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm166-3-3,
author = {M. Jasiczak},
title = {On boundary behaviour of the Bergman projection on pseudoconvex domains},
journal = {Studia Mathematica},
volume = {166},
year = {2005},
pages = {243-261},
zbl = {1066.32005},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm166-3-3}
}
M. Jasiczak. On boundary behaviour of the Bergman projection on pseudoconvex domains. Studia Mathematica, Tome 166 (2005) pp. 243-261. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm166-3-3/