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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) =∫0zf′(φ(ς ))g(ς ) . Given an admissible weight ω, the weighted Hilbert space Hω consists of all analytic functions f such that ∥f2Hω = |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 Hω using the ω-Carleson measures. Moreover, we give a lower bound for the essential norm of these operators.

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Periodical:
International Journal of Advanced Research in Mathematics (Volume 10)
Pages:
1-13
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
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References:

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