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Intrinsic Hardy–Orlicz spaces of conformal mappings
Pekka KoskelaSita Benedictsubject
Image domainPure mathematicsMathematics::Functional AnalysisMathematics - Complex VariablesmathematicsGeneral Mathematicsta111Mathematics::Classical Analysis and ODEsconforma mappingsConformal mapFunction (mathematics)Type (model theory)Space (mathematics)Path distanceUnit diskHardy–Orlicz spacesFOS: MathematicsComplex Variables (math.CV)30C35 (Primary) 30H10 (Secondary)Value (mathematics)Mathematicsdescription
We define a new type of Hardy-Orlicz spaces of conformal mappings on the unit disk where in place of the value |f(x)| we consider the intrinsic path distance between f(x) and f(0) in the image domain. We show that if the Orlicz function is doubling then these two spaces are actually the same, and we give an example when the intrinsic Hardy-Orlicz space is strictly smaller.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2014-09-23 | Bulletin of the London Mathematical Society |