Interpolating sequences of complex hyperplanes in the unit ball of ℂ n

Pascal J. Thomas

Annales de l'institut Fourier (1986)

  • Volume: 36, Issue: 3, page 167-181
  • ISSN: 0373-0956

Abstract

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A sufficient condition is given to make a sequence of hyperplanes in the complex unit ball an interpolating sequence for H ∞ , i.e. bounded holomorphic functions on the hyperplanes can be boundedly extended.

How to cite

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Thomas, Pascal J.. "Interpolating sequences of complex hyperplanes in the unit ball of ${\mathbb {C}}^n$." Annales de l'institut Fourier 36.3 (1986): 167-181. <http://eudml.org/doc/74722>.

@article{Thomas1986,
abstract = {A sufficient condition is given to make a sequence of hyperplanes in the complex unit ball an interpolating sequence for $H^\infty $, i.e. bounded holomorphic functions on the hyperplanes can be boundedly extended.},
author = {Thomas, Pascal J.},
journal = {Annales de l'institut Fourier},
keywords = {Carleson measures; unit ball; interpolating sequence for ; sequences of hyperplanes},
language = {eng},
number = {3},
pages = {167-181},
publisher = {Association des Annales de l'Institut Fourier},
title = {Interpolating sequences of complex hyperplanes in the unit ball of $\{\mathbb \{C\}\}^n$},
url = {http://eudml.org/doc/74722},
volume = {36},
year = {1986},
}

TY - JOUR
AU - Thomas, Pascal J.
TI - Interpolating sequences of complex hyperplanes in the unit ball of ${\mathbb {C}}^n$
JO - Annales de l'institut Fourier
PY - 1986
PB - Association des Annales de l'Institut Fourier
VL - 36
IS - 3
SP - 167
EP - 181
AB - A sufficient condition is given to make a sequence of hyperplanes in the complex unit ball an interpolating sequence for $H^\infty $, i.e. bounded holomorphic functions on the hyperplanes can be boundedly extended.
LA - eng
KW - Carleson measures; unit ball; interpolating sequence for ; sequences of hyperplanes
UR - http://eudml.org/doc/74722
ER -

References

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  1. [1] E. AMAR, Extension de fonctions analytiques avec estimation, Ark. Mat., 17, no. 1 (1979). Zbl0446.32004MR81a:46029
  2. [2] B. BERNDTSSON, An L∞-estimate for the ∂-equation in the unit ball of Cn, preprint, Göteborg, 1983. Zbl0523.32014
  3. [3] B. BERNDTSSON, Interpolating sequences for H∞ in the ball, Nederl. Akad. Wetensch. Indag. Math., 88 (1985). Zbl0588.32006MR87a:32007
  4. [4] L. CARLESON, An interpolation problem for bounded analytic functions, Amer. J. Math., 80 (1958), 921-930. Zbl0085.06504MR22 #8129
  5. [5] J. GARNETT, Bounded Analytic Functions, Academic Press, 1981. Zbl0469.30024MR83g:30037
  6. [6] M. HAKIM & N. SIBONY, Ensembles des zéros d'une fonction holomorphe bornée dans la boule unité, Math. Ann., 260, no. 4 (1982), 469-474. Zbl0499.32006MR83j:32001
  7. [7] W. RUDIN, Function Theory in the Unit Ball of Cn, Springer-Verlag, 1980. Zbl0495.32001MR82i:32002
  8. [8] H. SKODA, Valeurs au bord pour les solutions de l’opérateur d " et caractérisation des zéros des fonctions de la classe de Nevanlinna, Bull. Soc. Math. France, 104, no. 3 (1976), 225-299. Zbl0351.31007MR56 #8913
  9. [9] N. Th. VAROPOULOS, Ensembles pics et ensembles d'interpolation pour les algèbres uniformes, C.R.A.S., Paris, Sér. A, 272 (1970), 866-867. Zbl0214.13903
  10. [10] N. Th. VAROPOULOS, Sur un problème d'interpolation, C.R.A.S., Paris, Sér. A 274 (1972), 1539-1542. Zbl0236.41001

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