A note on the diagonal mapping in spaces of analytic functions in the unit polydisc

作者：Jevtic Miroljub^*; Pavlovic Miroslav; Shamoyan Romi F

来源：Publicationes Mathematicae-Debrecen, 2009, 74(1-2): 45-58.

• Bergman spaces
• mixed norm spaces on the polydisc
• diagonal mapping

We define two spaces K(p,q,alpha,beta) and M(p,alpha) of analytic functions in the unit polydisc U(n) of C(n), closely related to the mixed norm and the Bergman spaces on U(n), and for any holomorphic function F in K(p,q,alpha,beta) or in M(p-alpha) we consider its restriction to the diagonal, i.e., the function in the unit disc U of C defined by DF(z) = F(z,..., Z), and prove that the diagonal mapping D maps K(p,q,alpha,beta) onto the mixed-norm space H(p,q,beta+ q/p(vertical bar alpha vertical bar+2n-1)) (U) and the space M(p,alpha) onto the Bergman space A(p,vertical bar alpha vertical bar +2n-1) (U).

• 出版日期2009-1