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

Romi Shamoyan

Mathematica Bohemica (2008)

  • Volume: 133, Issue: 4, page 351-366
  • ISSN: 0862-7959

Abstract

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For any holomorphic function f on the unit polydisk 𝔻 n we consider its restriction to the diagonal, i.e., the function in the unit disc 𝔻 ⊂ ℂ defined by Diag f ( z ) = f ( z , ... , z ) , and prove that the diagonal map Diag maps the space Q p , q , s ( 𝔻 n ) of the polydisk onto the space Q ^ p , s , n q ( 𝔻 ) of the unit disk.

How to cite

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Shamoyan, Romi. "On some problems connected with diagonal map in some spaces of analytic functions." Mathematica Bohemica 133.4 (2008): 351-366. <http://eudml.org/doc/250527>.

@article{Shamoyan2008,
abstract = {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.},
author = {Shamoyan, Romi},
journal = {Mathematica Bohemica},
keywords = {diagonal map; holomorphic function; Bergman space; polydisk; diagonal map; holomorphic function; Bergman space; polydisk},
language = {eng},
number = {4},
pages = {351-366},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On some problems connected with diagonal map in some spaces of analytic functions},
url = {http://eudml.org/doc/250527},
volume = {133},
year = {2008},
}

TY - JOUR
AU - Shamoyan, Romi
TI - On some problems connected with diagonal map in some spaces of analytic functions
JO - Mathematica Bohemica
PY - 2008
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 133
IS - 4
SP - 351
EP - 366
AB - 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.
LA - eng
KW - diagonal map; holomorphic function; Bergman space; polydisk; diagonal map; holomorphic function; Bergman space; polydisk
UR - http://eudml.org/doc/250527
ER -

References

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