Weighted composition operators between weighted Bergman spaces and Hardy spaces on the unit ball of \(\mathbb C^{n}\). (English) Zbl 1114.32003

Luo, Luo; Ueki, Sei-Ichiro

J. Math. Anal. Appl. 326, No. 1, 88-100 (2007); corrigendum ibid. 342, No. 2, 1494 (2008).

The criteria for boundedness and compactness of weighted composition operators \(W_{\phi,\psi}:f\to\psi(f\circ\phi)\) acting in weighted Bergman spaces or in Hardy spaces on the unit ball of \(\mathbb{C}^n\) are obtained.

Reviewer: Dmitry Kaliuzhnyi-Verbovetskyi (Philadelphia)

MSC:

32A35	\(H^p\)-spaces, Nevanlinna spaces of functions in several complex variables
47B33	Linear composition operators
32A36	Bergman spaces of functions in several complex variables

Keywords:

weighted composition operators; weighted Bergman space; weighted Hardy space

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