On boundary behaviour of the Bergman projection on pseudoconvex domains

@article{M2005,
abstract = {It is shown that on strongly pseudoconvex domains the Bergman projection maps a space $Lv_\{k\}$ 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 $E ⊃ L^\{∞\}(Ω)$ defined by weighted-sup seminorms and equipped with the topology given by these seminorms, then E must contain the spaces $Lv_\{k\}$ 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 $L^\{∞\}$ 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.},
author = {M. Jasiczak},
journal = {Studia Mathematica},
keywords = {weighted-sup seminorms; asymptotic expansion},
language = {eng},
number = {3},
pages = {243-261},
title = {On boundary behaviour of the Bergman projection on pseudoconvex domains},
url = {http://eudml.org/doc/284624},
volume = {166},
year = {2005},
}

TY - JOUR
AU - M. Jasiczak
TI - On boundary behaviour of the Bergman projection on pseudoconvex domains
JO - Studia Mathematica
PY - 2005
VL - 166
IS - 3
SP - 243
EP - 261
AB - It is shown that on strongly pseudoconvex domains the Bergman projection maps a space $Lv_{k}$ 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 $E ⊃ L^{∞}(Ω)$ defined by weighted-sup seminorms and equipped with the topology given by these seminorms, then E must contain the spaces $Lv_{k}$ 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 $L^{∞}$ 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.
LA - eng
KW - weighted-sup seminorms; asymptotic expansion
UR - http://eudml.org/doc/284624
ER -