Complex symmetry of weighted composition operators in several variables

In this paper, we investigate analytic symbols [Formula: see text] and [Formula: see text] when the weighted composition operator [Formula: see text] is complex symmetric on general function space [Formula: see text]. As applications, we characterize completely the compactness, normality and isometry of complex symmetric weighted composition operators. Especially, we show that the equivalence of compactness and Hilbert–Schmidtness, and the existence of non-normal complex symmetric operators for such operators, which answers one open problem raised by Noor in [On an example of a complex symmetric composition operators on [Formula: see text], J. Funct. Anal. 269 (2015) 1899–1901] for higher dimensional case.

Weighted Composition Operators fromF(p,q,s)Spaces toHμ∞Spaces

LetH(B)denote the space of all holomorphic functions on the unit ballB. Letu∈H(B)andφbe a holomorphic self-map ofB. In this paper, we investigate the boundedness and compactness of the weighted composition operatoruCφfrom the general function spaceF(p,q,s)to the weighted-type spaceHμ∞in the unit ball.