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.
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Dyn’kin, E. (2000). Rational Functions in Bergman Spaces. In: Havin, V.P., Nikolski, N.K. (eds) Complex Analysis, Operators, and Related Topics. Operator Theory: Advances and Applications, vol 113. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8378-8_7
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DOI: https://doi.org/10.1007/978-3-0348-8378-8_7
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9541-5
Online ISBN: 978-3-0348-8378-8
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