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In this paper, we study weighted composition operators on Bergman spaces ofanalytic functions which are square integrable on polydisk. We develop thestudy in full generality, meaning that the corresponding weighted compositionoperators are not assumed to be bounded. The properties of weighted compositionoperators such as real symmetry, unitariness, complex symmetry, arecharacterized fully in simple algebraic terms, involving their symbols. As itturns out, a weighted composition operator having a symmetric structure must bebounded. We also obtain the interesting consequence that real symmetricweighted composition operators are complex symmetric corresponding an adaptedand highly relevant conjugation.

Real Symmetric, Unitary, And Complex Symmetric Weighted Composition Operators On Bergman Spaces Of Polydisk