Generalized Composition Operators on Weighted Hilbert Spaces of Analytic Functions

Al-Rawashdeh, Waleed

doi:10.18052/www.scipress.com/IJARM.10.1

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Generalized Composition Operators on Weighted Hilbert Spaces of Analytic Functions

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Abstract:

Let φ be an analytic self-map of the open unit disk D and g be an analytic function on D. The generalized composition operator induced by the maps g and φ is defined by the integral operator I(g,φ)f(z) =∫₀^zf′(φ(ς ))g(ς )dς . Given an admissible weight ω, the weighted Hilbert space H_ω consists of all analytic functions f such that ∥f∥²_Hω = |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 space H_ω using the ω-Carleson measures. Moreover, we give a lower bound for the essential norm of these operators.

Info:

Periodical:

International Journal of Advanced Research in Mathematics (Volume 10)

Pages:

1-13

DOI:

https://doi.org/10.18052/www.scipress.com/IJARM.10.1

Citation:

W. Al-Rawashdeh, "Generalized Composition Operators on Weighted Hilbert Spaces of Analytic Functions", International Journal of Advanced Research in Mathematics, Vol. 10, pp. 1-13, 2017

Online since:

September 2017

Authors:

Waleed Al-Rawashdeh

Keywords:

(Vanishing) ω-Carleson Measure, Bounded Operators, Compact Operators, Essential Norm, Generalized Composition Operators, Weighted Hilbert Spaces

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Open Access

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Creative Commons Attribution 4.0 International License

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