Kucik, AS (2017) Carleson measures for Hilbert spaces of analytic functions on the complex half-plane. Journal of Mathematical Analysis and Applications, 445 (1). pp. 476-497. ISSN 0022-247X
Abstract
The notion of a Carleson measure was introduced by Lennart Carleson in his proof of the Corona Theorem for H∞(D). In this paper we will define it for certain type of reproducing kernel Hilbert spaces of analytic functions of the complex half-plane, C+, which will include Hardy, Bergman and Dirichlet spaces. We will obtain several necessary or sufficient conditions for a positive Borel measure to be Carleson by preforming tests on reproducing kernels, weighted Bergman kernels, and studying the tree model obtained from a decomposition of the complex half-plane. The Dirichlet space will be investigated in detail as a special case. Finally, we will present a control theory application of Carleson measures in determining admissibility of controls in well-posed linear evolution equations.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2016, Elsevier. This is an author produced version of a paper published in Journal of Mathematical Analysis and Applications. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Carleson measures; Reproducing kernel Hilbert spaces; Dirichlet space; Control operators; Admissibility; Laplace transform |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Pure Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 06 Sep 2016 08:17 |
Last Modified: | 14 Aug 2017 07:16 |
Published Version: | http://dx.doi.org/10.1016/j.jmaa.2016.08.019 |
Status: | Published |
Publisher: | Elsevier |
Identification Number: | 10.1016/j.jmaa.2016.08.019 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:104261 |