Geodesic
On some problems connected with diagonal map in some spaces of analytic functions
Mathematica Bohemica, Tome 133 (2008) no. 4, pp. 351-366

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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 $\mathop{\rm Diag} f(z)=f(z,\ldots ,z)$, and prove that the diagonal map ${\rm Diag}$ maps the space $Q_{p,q,s}(\mathbb D ^n)$ of the polydisk onto the space $\widehat Q^q_{p,s,n}(\mathbb D )$ of the unit disk.
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 $\mathop{\rm Diag} f(z)=f(z,\ldots ,z)$, and prove that the diagonal map ${\rm Diag}$ maps the space $Q_{p,q,s}(\mathbb D ^n)$ of the polydisk onto the space $\widehat Q^q_{p,s,n}(\mathbb D )$ of the unit disk.
DOI : 10.21136/MB.2008.140625
Classification : 30H05, 47B35
Keywords: diagonal map; holomorphic function; Bergman space; polydisk 
Shamoyan, Romi. On some problems connected with diagonal map in some spaces of analytic functions. Mathematica Bohemica, Tome 133 (2008) no. 4, pp. 351-366. doi: 10.21136/MB.2008.140625
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