Pointwise multipliers and corona type decomposition in $BMOA$
Annales de l'Institut Fourier, Tome 46 (1996) no. 1, p. 111-137
Dans cet article nous obtenons plusieurs caractérisations des multiplicateurs ponctuels de l’espace $BMOA$ dans la boule unité $B$ de ${ℂ}^{n}$. De plus, si ${g}_{1},...,{g}_{m}$ sont des fonctions holomorphes dans $B$ nous démontrons que l’application ${M}_{g}\left(f\right)\left(z\right)=\sum _{j=1}^{m}\phantom{\rule{0.166667em}{0ex}}{g}_{j}\left(z\right)\phantom{\rule{0.166667em}{0ex}}{f}_{j}\left(z\right)$ envoie $BMOA×...×BMOA$ sur $BMOA$ si et seulement si les fonctions ${g}_{j}$ sont multiplicateurs de l’espace $BMOA$ et satisfont $\sum _{j=1}^{m}\phantom{\rule{0.166667em}{0ex}}|{g}_{j}\left(z\right)|\ge \delta >0.$
In this paper we obtain several characterizations of the pointwise multipliers of the space $BMOA$ in the unit ball $B$ of ${ℂ}^{n}$. Moreover, if ${g}_{1},...,{g}_{m}$ are holomorphic functions on $B$, we prove that ${M}_{g}\left(f\right)\left(z\right)=\sum _{j=1}^{m}\phantom{\rule{0.166667em}{0ex}}{g}_{j}\left(z\right)\phantom{\rule{0.166667em}{0ex}}{f}_{j}\left(z\right)$ maps $BMOA×...×BMOA$ onto $BMOA$ if and only if the functions ${g}_{j}$ are multipliers of the space $BMOA$ and satisfy $\sum _{j=1}^{m}\phantom{\rule{0.166667em}{0ex}}|{g}_{j}\left(z\right)|\ge \delta >0.$
@article{AIF_1996__46_1_111_0,
author = {Ortega, J. M. and F\abrega, Joan},
title = {Pointwise multipliers and corona type decomposition in $BMOA$},
journal = {Annales de l'Institut Fourier},
publisher = {Association des Annales de l'institut Fourier},
volume = {46},
number = {1},
year = {1996},
pages = {111-137},
doi = {10.5802/aif.1509},
zbl = {0840.32001},
mrnumber = {97k:32009},
language = {en},
url = {http://www.numdam.org/item/AIF_1996__46_1_111_0}
}

Ortega, J. M.; Fàbrega, Joan. Pointwise multipliers and corona type decomposition in $BMOA$. Annales de l'Institut Fourier, Tome 46 (1996) no. 1, pp. 111-137. doi : 10.5802/aif.1509. http://www.numdam.org/item/AIF_1996__46_1_111_0/`

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