Let be a sequence in the upper half plane. If and if
has solution in the class of Poisson integrals of functions for any sequence , then we show that is an interpolating sequence for . If , has solution in the class of Poisson integrals of BMO functions whenever , then is again an interpolating sequence for . A somewhat more general theorem is also proved and a counterexample for the case is described.
Soit une suite de points du demi-plan supérieur ; si, pour tel que , et pour toute suite dans il existe une fonction , intégrale de poisson d’une fonction de qui vérifie :
alors nous montrons que est une suite d’interpolation pour . De même, si on fait l’hypothèse qu’il existe une solution , intégrale de Poisson d’une fonction de BMO qui vérifie avec et dans , est encore une suite d’interpolation pour .
Un théorème un peu plus général est prouvé et on donne un contre-exemple dans le cas où .
@article{AIF_1978__28_4_215_0, author = {Garnett, John B.}, title = {Harmonic interpolating sequences, $L^p$ and {BMO}}, journal = {Annales de l'Institut Fourier}, pages = {215--228}, publisher = {Institut Fourier}, address = {Grenoble}, volume = {28}, number = {4}, year = {1978}, doi = {10.5802/aif.721}, mrnumber = {80g:30024}, zbl = {0377.46044}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/aif.721/} }
TY - JOUR AU - Garnett, John B. TI - Harmonic interpolating sequences, $L^p$ and BMO JO - Annales de l'Institut Fourier PY - 1978 SP - 215 EP - 228 VL - 28 IS - 4 PB - Institut Fourier PP - Grenoble UR - http://archive.numdam.org/articles/10.5802/aif.721/ DO - 10.5802/aif.721 LA - en ID - AIF_1978__28_4_215_0 ER -
Garnett, John B. Harmonic interpolating sequences, $L^p$ and BMO. Annales de l'Institut Fourier, Volume 28 (1978) no. 4, pp. 215-228. doi : 10.5802/aif.721. http://archive.numdam.org/articles/10.5802/aif.721/
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