Pointwise multipliers and corona type decomposition in B M O A

J. M. Ortega; Joan Fàbrega

Annales de l'institut Fourier (1996)

  • Volume: 46, Issue: 1, page 111-137
  • ISSN: 0373-0956

Abstract

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In this paper we obtain several characterizations of the pointwise multipliers of the space B M O A in the unit ball B of ℂ n . Moreover, if g 1 , ... , g m are holomorphic functions on B , we prove that M g ( f ) ( z ) = ∑ j = 1 m g j ( z ) f j ( z ) maps B M O A × ... × B M O A onto B M O A if and only if the functions g j are multipliers of the space B M O A and satisfy ∑ j = 1 m | g j ( z ) | ≥ δ > 0 .

How to cite

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Ortega, J. M., and Fàbrega, Joan. "Pointwise multipliers and corona type decomposition in $BMOA$." Annales de l'institut Fourier 46.1 (1996): 111-137. <http://eudml.org/doc/75168>.

@article{Ortega1996,
abstract = {In this paper we obtain several characterizations of the pointwise multipliers of the space $BMOA$ in the unit ball $B$ of $\{\Bbb C\}^n$. Moreover, if $g_1,\ldots ,g_m$ are holomorphic functions on $B$, we prove that $M_g(f)(z)=\sum \limits _\{j=1\}^m\,g_j(z)\,f_j(z)$ maps $BMOA\times \ldots \times BMOA$ onto $BMOA$ if and only if the functions $g_j$ are multipliers of the space $BMOA$ and satisfy $\sum \limits _\{j=1\}^m\,\vert g_j(z)\vert \ge \delta &gt;0.$},
author = {Ortega, J. M., Fàbrega, Joan},
journal = {Annales de l'institut Fourier},
keywords = {; pointwise multipliers; corona problem},
language = {eng},
number = {1},
pages = {111-137},
publisher = {Association des Annales de l'Institut Fourier},
title = {Pointwise multipliers and corona type decomposition in $BMOA$},
url = {http://eudml.org/doc/75168},
volume = {46},
year = {1996},
}

TY - JOUR
AU - Ortega, J. M.
AU - Fàbrega, Joan
TI - Pointwise multipliers and corona type decomposition in $BMOA$
JO - Annales de l'institut Fourier
PY - 1996
PB - Association des Annales de l'Institut Fourier
VL - 46
IS - 1
SP - 111
EP - 137
AB - In this paper we obtain several characterizations of the pointwise multipliers of the space $BMOA$ in the unit ball $B$ of ${\Bbb C}^n$. Moreover, if $g_1,\ldots ,g_m$ are holomorphic functions on $B$, we prove that $M_g(f)(z)=\sum \limits _{j=1}^m\,g_j(z)\,f_j(z)$ maps $BMOA\times \ldots \times BMOA$ onto $BMOA$ if and only if the functions $g_j$ are multipliers of the space $BMOA$ and satisfy $\sum \limits _{j=1}^m\,\vert g_j(z)\vert \ge \delta &gt;0.$
LA - eng
KW - ; pointwise multipliers; corona problem
UR - http://eudml.org/doc/75168
ER -

References

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