On Laplace-Carleson embedding theorems

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Abstract

This paper gives embedding theorems for a very general class of weighted Bergman spaces: the results include a number of classical Carleson embedding theorems as special cases. The little Hankel operators on these Bergman spaces are also considered. Next, a study is made of Carleson embeddings in the right half-plane induced by taking the Laplace transform of functions defined on the positive half-line (these embeddings have applications in control theory): particular attention is given to the case of a sectorial measure or a measure supported on a strip, and complete necessary and sufficient conditions for a bounded embedding are given in many cases. (C) 2012 Elsevier Inc. All rights reserved.

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Research areas and keywords

Subject classification (UKÄ) – MANDATORY

  • Mathematics

Keywords

  • Hardy space, Weighted Bergman space, Laplace transform, Carleson measure
Original languageEnglish
Pages (from-to)783-814
JournalJournal of Functional Analysis
Volume264
Issue number3
Publication statusPublished - 2013
Publication categoryResearch
Peer-reviewedYes