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Vietnam Journal of Mathematics 34:3(2006) 255-264  Weighted Composition Operators Between Different Weighted Bergman Spaces in Polydiscs Li Songxiao Abstract.  Let $D^n$ be the unit polydiscs of $\mathbb C^n$, $\varphi(z)=(\varphi_1(z),\ldots, \varphi_n(z))$ be a holomorphic self-map of $D^n$ and $\psi(z)$ a holomorphic function on $D^n$. Necessary and sufficient conditions are established for the weighted composition operator $\psi C_\varphi$ induced by $\varphi(z)$ and $\psi(z)$ to be bounded or compact between different weighted Bergman spaces in polydiscs.   2000 Mathematics Subject Classification: 47B38, 32A36. Keywords: Bergman space, polydiscs, weighted composition operator.

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