Hölder functions in Bergman type spaces

Yingwei Chen, and Guangbin Ren. "Hölder functions in Bergman type spaces." Studia Mathematica 212.3 (2012): 237-258. <http://eudml.org/doc/285586>.

@article{YingweiChen2012,
abstract = {It seems impossible to extend the boundary value theory of Hardy spaces to Bergman spaces since there is no boundary value for a function in a Bergman space in general. In this article we provide a new idea to show what is the correct version of Bergman spaces by demonstrating the extension to Bergman spaces of a result of Hardy-Littlewood in Hardy spaces, which characterizes the Hölder class of boundary values for a function from Hardy spaces in the unit disc in terms of the growth of its derivative. To this end, a class of Hölder functions in Bergman spaces is introduced in terms of the modulus of continuity and we establish its characterization in terms of radial derivatives. The classical result of Hardy-Littlewood in the Hardy space can be thought of as the limit case, matching the fact that the Hardy space is a limit of Bergman spaces.},
author = {Yingwei Chen, Guangbin Ren},
journal = {Studia Mathematica},
keywords = {Bergman spaces; modulus of continuity; bounded symmetry domains},
language = {eng},
number = {3},
pages = {237-258},
title = {Hölder functions in Bergman type spaces},
url = {http://eudml.org/doc/285586},
volume = {212},
year = {2012},
}

TY - JOUR
AU - Yingwei Chen
AU - Guangbin Ren
TI - Hölder functions in Bergman type spaces
JO - Studia Mathematica
PY - 2012
VL - 212
IS - 3
SP - 237
EP - 258
AB - It seems impossible to extend the boundary value theory of Hardy spaces to Bergman spaces since there is no boundary value for a function in a Bergman space in general. In this article we provide a new idea to show what is the correct version of Bergman spaces by demonstrating the extension to Bergman spaces of a result of Hardy-Littlewood in Hardy spaces, which characterizes the Hölder class of boundary values for a function from Hardy spaces in the unit disc in terms of the growth of its derivative. To this end, a class of Hölder functions in Bergman spaces is introduced in terms of the modulus of continuity and we establish its characterization in terms of radial derivatives. The classical result of Hardy-Littlewood in the Hardy space can be thought of as the limit case, matching the fact that the Hardy space is a limit of Bergman spaces.
LA - eng
KW - Bergman spaces; modulus of continuity; bounded symmetry domains
UR - http://eudml.org/doc/285586
ER -