On Laplace-Carleson embedding theorems

Details On Laplace-Carleson embedding theorems On Laplace-Carleson embedding theorems

2012-01-04

arxiv.org/abs/1201.1021v1

Mathematics

Functional Analysis

26 pages, 1 figure

Scientific paper

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. 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.

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