On some problems connected with diagonal map
in some spaces of analytic functions

Abstract: For any holomorphic function $f$ on the unit polydisk $\DD^n$ we consider its restriction to the diagonal, i.e., the function in the unit disc $\DD\subset\CC$ defined by $\Diag f(z)=f(z,\ldots,z)$, and prove that the diagonal map $\Diag$ maps the space $Q_{p,q,s}(\DD^n)$ of the polydisk onto the space $\widehat Q^q_{p,s,n}(\DD)$ of the unit disk.

Keywords: diagonal map, holomorphic function, Bergman space, polydisk

Classification (MSC2000): 47B35, 30H05

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