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- W4303071128 abstract "The notion of a Carleson measure was introduced by Lennart Carleson in his proof of the Corona Theorem for $H^infty(mathbb{D})$. In this paper we will define it for certain type of reproducing kernel Hilbert spaces of analytic functions of the complex half-plane, $mathbb{C}_+$, 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." @default.
- W4303071128 created "2022-10-07" @default.
- W4303071128 creator A5009418320 @default.
- W4303071128 date "2016-04-20" @default.
- W4303071128 modified "2023-09-27" @default.
- W4303071128 title "Carleson measures for Hilbert spaces of analytic functions on the complex half-plane" @default.
- W4303071128 doi "https://doi.org/10.48550/arxiv.1604.06015" @default.
- W4303071128 hasPublicationYear "2016" @default.
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