کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
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4614063 | 1339279 | 2017 | 22 صفحه PDF | دانلود رایگان |
The notion of a Carleson measure was introduced by Lennart Carleson in his proof of the Corona Theorem for H∞(D)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+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.
Journal: Journal of Mathematical Analysis and Applications - Volume 445, Issue 1, 1 January 2017, Pages 476–497