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

Shamoyan, Romi

Mathematica Bohemica, Tome 133 (2008) no. 4, pp. 351-366.

Résumé

For any holomorphic function $f$ on the unit polydisk ${\mathbb{D}}^n$ we consider its restriction to the diagonal, i.e., the function in the unit disc $\mathbb{D}\subset \mathbb{C}$ defined by $\mathrm{Diag}f(z)=f(z,\dots ,z)$, and prove that the diagonal map $\mathrm{D}\mathrm{i}\mathrm{a}\mathrm{g}$ maps the space $Q_{p,q,s}({\mathbb{D}}^n)$ of the polydisk onto the space ${\hat{Q}}_{p,s,n}^q(\mathbb{D})$ of the unit disk.

Détail

DOI : 10.21136/MB.2008.140625

Classification : 30H05, 47B35
Mots-clés : diagonal map; holomorphic function; Bergman space; polydisk