ω –weighted holomorphic Besov spaces on the unit ball in C n

A. V. Harutyunyan; Wolfgang Lusky

Commentationes Mathematicae Universitatis Carolinae (2011)

  • Volume: 52, Issue: 1, page 37-56
  • ISSN: 0010-2628

Abstract

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The ω -weighted Besov spaces of holomorphic functions on the unit ball B n in C n are introduced as follows. Given a function ω of regular variation and 0 < p < , a function f holomorphic in B n is said to belong to the Besov space B p ( ω ) if f B p ( ω ) p = B n ( 1 - | z | 2 ) p | D f ( z ) | p ω ( 1 - | z | ) ( 1 - | z | 2 ) n + 1 d ν ( z ) < + , where d ν ( z ) is the volume measure on B n and D stands for the fractional derivative of f . The holomorphic Besov space is described in the terms of the corresponding L p ( ω ) space. Some projection theorems and theorems on existence of the inversions of these projections are proved. Also, explicit descriptions of the duals of the considered Besov spaces are given.

How to cite

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Harutyunyan, A. V., and Lusky, Wolfgang. "$\omega $–weighted holomorphic Besov spaces on the unit ball in $C^n$." Commentationes Mathematicae Universitatis Carolinae 52.1 (2011): 37-56. <http://eudml.org/doc/246848>.

@article{Harutyunyan2011,
abstract = {The $\omega $-weighted Besov spaces of holomorphic functions on the unit ball $B^n$ in $C^n$ are introduced as follows. Given a function $\omega $ of regular variation and $0< p< \infty $, a function $f$ holomorphic in $B^n$ is said to belong to the Besov space $B_p(\omega )$ if \[ \Vert f\Vert ^p\_\{B\_p(\omega )\}=\int \_\{B^n\} (1-|z|^2)^p|Df(z)|^p \frac\{\omega (1-|z|)\}\{(1-|z|^2)^\{n+1\}\}\,d\nu (z)< +\infty , \] where $d\nu (z)$ is the volume measure on $B^n$ and $D$ stands for the fractional derivative of $f$. The holomorphic Besov space is described in the terms of the corresponding $L_p(\omega )$ space. Some projection theorems and theorems on existence of the inversions of these projections are proved. Also, explicit descriptions of the duals of the considered Besov spaces are given.},
author = {Harutyunyan, A. V., Lusky, Wolfgang},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {weighted Besov spaces; unit ball; projection; weighted Besov space; unit ball; projection; holomorphic function},
language = {eng},
number = {1},
pages = {37-56},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {$\omega $–weighted holomorphic Besov spaces on the unit ball in $C^n$},
url = {http://eudml.org/doc/246848},
volume = {52},
year = {2011},
}

TY - JOUR
AU - Harutyunyan, A. V.
AU - Lusky, Wolfgang
TI - $\omega $–weighted holomorphic Besov spaces on the unit ball in $C^n$
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2011
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 52
IS - 1
SP - 37
EP - 56
AB - The $\omega $-weighted Besov spaces of holomorphic functions on the unit ball $B^n$ in $C^n$ are introduced as follows. Given a function $\omega $ of regular variation and $0< p< \infty $, a function $f$ holomorphic in $B^n$ is said to belong to the Besov space $B_p(\omega )$ if \[ \Vert f\Vert ^p_{B_p(\omega )}=\int _{B^n} (1-|z|^2)^p|Df(z)|^p \frac{\omega (1-|z|)}{(1-|z|^2)^{n+1}}\,d\nu (z)< +\infty , \] where $d\nu (z)$ is the volume measure on $B^n$ and $D$ stands for the fractional derivative of $f$. The holomorphic Besov space is described in the terms of the corresponding $L_p(\omega )$ space. Some projection theorems and theorems on existence of the inversions of these projections are proved. Also, explicit descriptions of the duals of the considered Besov spaces are given.
LA - eng
KW - weighted Besov spaces; unit ball; projection; weighted Besov space; unit ball; projection; holomorphic function
UR - http://eudml.org/doc/246848
ER -

References

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