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Weighted composition operators from Bergman-type spaces into Bloch spaces

Authors:

Affiliation:

(1) Department of Mathematics, Shantou University, 515 063 Shantou, Guangdong, China;(2) Department of Mathematics, Jia Ying University, 514 015 Meizhou, Guangdong, China;(3) Mathematical Institute of the Serbian Academy of Science, Knez Mihailova 35/I, 11000 Beograd, Serbia

Abstract:

Let ϕ be an analytic self-map and u be a fixed analytic function on the open unit disk D in the complex plane ℂ. The weighted composition operator is defined by

$$
uC_phi f = u cdot (f circ phi ), f in H(D).
$$

Weighted composition operators from Bergman-type spaces into Bloch spaces and little Bloch spaces are characterized by function theoretic properties of their inducing maps.

Keywords:

Weighted composition operator Bergman-type space Bloch space

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