Pointwise multipliers and corona type decomposition in $BMOA$

Ortega, J. M.; Fàbrega, Joan

doi:10.5802/aif.1509

Pointwise multipliers and corona type decomposition in

B M O A

Ortega, J. M. ; Fàbrega, Joan

Annales de l'Institut Fourier, Tome 46 (1996) no. 1, pp. 111-137.

Résumé
Abstract

Dans cet article nous obtenons plusieurs caractérisations des multiplicateurs ponctuels de l’espace $B M O A$ 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 $M_{g} (f) (z) = \sum_{j = 1}^{m} g_{j} (z) f_{j} (z)$ envoie $B M O A \times ... \times B M O A$ sur $B M O A$ si et seulement si les fonctions $g_{j}$ sont multiplicateurs de l’espace $B M O A$ et satisfont $\sum_{j = 1}^{m} | g_{j} (z) | \geq δ > 0 .$

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 $M_{g} (f) (z) = \sum_{j = 1}^{m} g_{j} (z) f_{j} (z)$ maps $B M O A \times ... \times B M O A$ onto $B M O A$ if and only if the functions $g_{j}$ are multipliers of the space $B M O A$ and satisfy $\sum_{j = 1}^{m} | g_{j} (z) | \geq δ > 0 .$

MR Zbl

DOI : 10.5802/aif.1509

@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},
     pages = {111--137},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     volume = {46},
     number = {1},
     year = {1996},
     doi = {10.5802/aif.1509},
     mrnumber = {97k:32009},
     zbl = {0840.32001},
     language = {en},
     url = {https://www.numdam.org/articles/10.5802/aif.1509/}
}

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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. https://www.numdam.org/articles/10.5802/aif.1509/

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