Norm Inequalities for Weighted Dirichlet Spaces with Applications to Conformal Maps
Abstract
Abstract A variety of norm inequalities related to Bergman and Dirichlet spaces induced by radial weights is established. Some of the results obtained can be considered as generalizations of certain known special cases while most of the estimates discovered are completely new. In particular, a Littlewood-Paley estimate recently proved by Peláez and the second author (Peláez and Rättyä Adv. Math. , 391 , 70, 2021) is improved in part. The second objective of the paper is to apply the obtained norm inequalities to relate the growth of the maximum modulus of a conformal map f , measured in terms of a weighted integrability condition, to a geometric quantity involving the area of image under f of a disc centered at the origin. Our findings in this direction yield new geometric characterizations of conformal maps in certain weighted Dirichlet and Besov spaces.
Fields of Study & Subjects
Holomorphic and Operator Theory
Analytic and geometric function theory
Meromorphic and Entire Functions
Publication details
- Journal / source
- Potential Analysis
- Publisher
- Springer Science and Business Media LLC
- Volume
- 64
- Issue
- 3
- Publication date
- 27 February 2026
- Language
- EN
- Document type
- Book chapter