Harmonic interpolating sequences, $L^p$ and BMO

Garnett, John B.. "Harmonic interpolating sequences, $L^p$ and BMO." Annales de l'institut Fourier 28.4 (1978): 215-228. <http://eudml.org/doc/74382>.

@article{Garnett1978,
abstract = {Let $(z_\nu )$ be a sequence in the upper half plane. If $1&lt; p\le \infty $ and if\begin\{\}y^\{1/p\}\_\nu f(z\_\nu ) = a\_\nu ,~\nu =1,2,\ldots \qquad (*)\end\{\}has solution $f(z)$ in the class of Poisson integrals of $L^p$ functions for any sequence $(a_\nu ) \in \ell ^p$, then we show that $(z_\nu )$ is an interpolating sequence for $H^\infty $. If $f(z_\nu ) = a_\nu $, $\nu =1,2,\ldots $ has solution in the class of Poisson integrals of BMO functions whenever $(a_\nu ) \in \ell ^\infty $, then $(z_\nu )$ is again an interpolating sequence for $H^\infty $. A somewhat more general theorem is also proved and a counterexample for the case $p\le 1$ is described.},
author = {Garnett, John B.},
journal = {Annales de l'institut Fourier},
language = {eng},
number = {4},
pages = {215-228},
publisher = {Association des Annales de l'Institut Fourier},
title = {Harmonic interpolating sequences, $L^p$ and BMO},
url = {http://eudml.org/doc/74382},
volume = {28},
year = {1978},
}

TY - JOUR
AU - Garnett, John B.
TI - Harmonic interpolating sequences, $L^p$ and BMO
JO - Annales de l'institut Fourier
PY - 1978
PB - Association des Annales de l'Institut Fourier
VL - 28
IS - 4
SP - 215
EP - 228
AB - Let $(z_\nu )$ be a sequence in the upper half plane. If $1&lt; p\le \infty $ and if\begin{}y^{1/p}_\nu f(z_\nu ) = a_\nu ,~\nu =1,2,\ldots \qquad (*)\end{}has solution $f(z)$ in the class of Poisson integrals of $L^p$ functions for any sequence $(a_\nu ) \in \ell ^p$, then we show that $(z_\nu )$ is an interpolating sequence for $H^\infty $. If $f(z_\nu ) = a_\nu $, $\nu =1,2,\ldots $ has solution in the class of Poisson integrals of BMO functions whenever $(a_\nu ) \in \ell ^\infty $, then $(z_\nu )$ is again an interpolating sequence for $H^\infty $. A somewhat more general theorem is also proved and a counterexample for the case $p\le 1$ is described.
LA - eng
UR - http://eudml.org/doc/74382
ER -