Essential norm of weighted composition operators on Bargmann-Fock spaces

Waleed Al-Rawashdeh

Abstract


Let ϕ be an entire self-map of the n-dimensional Euclidean complex space Cn and ψ be an entire function on Cn. A weighted composition operator induced by ϕ with weight ψ is given by (Wψ,ϕf)(z) = ψ(z)f(ϕ(z)), for z∈Cn and f is entire function on Cn. In this paper, we study weighted composition operators between Bargmann-Fock spaces Fpα(Cn) and Fpα(Cn) for 0 < p,q < ∞. Using Carleson-type measures techniques, we characterize the boundedness and compactness of these operators, when 0 < p,q < ∞. We also obtained an estimate of the essential norm of these operators, when 1 < p ≤ q < ∞. The results written in terms of a certain Berezin-type integral transform on Cn.

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Published: 2015-04-17

How to Cite this Article:

Waleed Al-Rawashdeh, Essential norm of weighted composition operators on Bargmann-Fock spaces, Advances in Inequalities and Applications, Vol 2015 (2015), Article ID 6

Copyright © 2015 Waleed Al-Rawashdeh. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Advances in Inequalities and Applications

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