Rational Functions in Bergman Spaces

Abstract

An inversion of the classical Hardy-Littlewood theorem on embedding of Hardy spaces into Bergman spaces is proved for the subset of rational functions of a given degree. Many other embeddings for such functions follow from this result. For the Hardy-Littlewood theorem itself, a refinement in terms of rational approximation is proved. As an application, a sharp rational approximation theorem in the Bergman norm is obtained.KeywordsRational FunctionHardy SpaceRational ApproximationBesov SpaceBergman SpaceThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.