UNITARY, SELF–ADJOINT AND J −SYMMETRIC WEIGHTED COMPOSITION OPERATORS ON FOCK–SOBOLEV SPACES.

In this paper, we characterize the boundedness and compactness for weighted composition operators on the Fock-Sobolev space F ^p,m(Cⁿ), 0 < p < ∞. We prove that no nontrivial unitary or self-adjoint weighted composition operators exist on F^2,m(Cⁿ) when m ≥ 1. As an application, we also prove that there exist only trivial J -symmetric weighted composition operators on F^2,m(Cⁿ) when m ≥ 1. [ABSTRACT FROM AUTHOR]