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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 Dn be the unit polydiscs of Cn, j(z) = (j1(z), , jn(z)) be a holomorphic self-map of Dn and y(z) a holomorphic function on Dn. Necessary and sufficient conditions are established for the weighted composition operator yCj induced by j(z) and y(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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