On Laplace-Carleson embedding theorems
Functional Analysis
2012-10-11 v2 Classical Analysis and ODEs
Complex Variables
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. We also consider little Hankel operators on these Bergman spaces. 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.
Cite
@article{arxiv.1201.1021,
title = {On Laplace-Carleson embedding theorems},
author = {Birgit Jacob and Jonathan Partington and Sandra Pott},
journal= {arXiv preprint arXiv:1201.1021},
year = {2012}
}
Comments
26 pages, 1 figure