Carleson measures for Hilbert spaces of analytic functions on the complex half-plane

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:445

Article

Kucik, Andrzej S.¹ 

[1] Univ Leeds, Sch Math, Leeds LS2 9JT, W Yorkshire, England

关键词: Carleson measures;    Reproducing kernel Hilbert spaces;    Dirichlet space;    Control operators;    Admissibility;    Laplace transform;   

DOI  :  10.1016/j.jmaa.2016.08.019

来源: Elsevier

【 摘 要 】

The notion of a Carleson measure was introduced by Lennart Carleson in his proof of the Corona Theorem for H-infinity(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. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free