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

2017 ◽  
Vol 445 (1) ◽  
pp. 476-497 ◽  
Author(s):  
Andrzej S. Kucik
Keyword(s):  
Half Plane ◽  
Hilbert Spaces ◽  
Analytic Functions ◽  
Carleson Measures ◽  
Complex Half Plane ◽  
Spaces Of Analytic Functions

Generalized Composition Operators on Weighted Hilbert Spaces of Analytic Functions

2017 ◽  
Vol 10 ◽  
pp. 1-13 ◽  
Author(s):  
Waleed Al-Rawashdeh
Keyword(s):  
Hilbert Space ◽  
Hilbert Spaces ◽  
Analytic Functions ◽  
Composition Operators ◽  
Essential Norm ◽  
Carleson Measures ◽  
Open Unit ◽  
Open Unit Disk ◽  
Admissible Weight ◽  
Spaces Of Analytic Functions

Letφbe an analytic self-map of the open unit disk D andgbe an analytic function on D. The generalized composition operator induced by the mapsgandφis defined by the integral operatorI(g,φ)f(z) =∫0zf′(φ(ς))g(ς)dς. Given an admissible weightω, the weighted Hilbert spaceHωconsists of all analytic functionsfsuch that ∥f∥2Hω= |f(0)|2+∫D|f′(z)|2ω(z)dA(z) is finite. In this paper, we characterize the boundedness and compactness of the generalized composition operators on the spaceHωusing theω-Carleson measures. Moreover, we give a lower bound for the essential norm of these operators.

scholarly journals Comparison of singular numbers of composition operators on different Hilbert spaces of analytic functions

2021 ◽  
Vol 280 (3) ◽  
pp. 108834
Author(s):  
Pascal Lefèvre ◽  
Daniel Li ◽  
Hervé Queffélec ◽  
Luis Rodríguez-Piazza
Keyword(s):  
Hilbert Spaces ◽  
Analytic Functions ◽  
Composition Operators ◽  
Singular Numbers ◽  
Spaces Of Analytic Functions
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