Dirichlet and VMOA domains via Schwarzian derivative

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:359

Article

Perez-Gonzalez, Fernando¹  Rattya, Jouni² 

[1] Univ La Laguna, Dept Anal Matemat, Tenerife 39271, Spain

[2] Univ Joensuu, Dept Math & Phys, FIN-80101 Joensuu, Finland

关键词: Schwarzian derivative;    Conformal map;    Carleson measure;    Dirichlet space;    Besov space;    BMOA;    VMOA;    Q(p);    Q(p.0);   

DOI  :  10.1016/j.jmaa.2009.06.023

来源: Elsevier

【 摘 要 】

Short proofs of the following results concerning a bounded conformal map g of the unit disc D are presented: (1) log g' belongs to the Dirichlet space if and only if the Schwarzian derivative S-g of g Satisfies S-g(z)(1 - vertical bar z vertical bar(2)) is an element of L-2(D): (2) log g' is an element of VMOA if and only if vertical bar S-g(z)vertical bar(2)(1 - vertical bar z vertical bar(2))(3) is a vanishing Carleson measure on D. Analogous results for Besov and Q(p,0) spaces are also given. (C) 2009 Elsevier Inc. All rights reserved.

【 授权许可】

Free