Complex symmetry of weighted composition operators in several variables

In this paper, we investigate analytic symbols psi and phi when the weighted composition operator C-psi,C-phi is complex symmetric on general function space H-s. 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 H-2( D), J. Funct. Anal. 269 (2015) 1899-1901] for higher dimensional case.