Hölder functions in Bergman type spaces

• Autorzy: Yingwei Chen , Guangbin Ren
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 32A36: Bergman spaces
• 26A16: Lipschitz (H\"older) classes

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2012
• Tom: 212
• Numer: 3
• Strony: 237-258

Daty

wydano

2012

Twórcy

autor

Yingwei Chen

• College of Mathematics and Statistics, Hebei University of Economics and Business, 050061 Shijiazhuang, China

autor

Guangbin Ren

• School of Mathematical Sciences, University of Science and Technology of China, 230026 Hefei, China

Identyfikatory

DOI

10.4064/sm212-3-3