On Hardy spaces in complex ellipsoids

Hansson, Thomas. "On Hardy spaces in complex ellipsoids." Annales de l'institut Fourier 49.5 (1999): 1477-1501. <http://eudml.org/doc/75391>.

@article{Hansson1999,
abstract = {This paper deals with atomic decomposition and factorization of functions in the holomorphic Hardy space $H^\{1\}$. Such representation theorems have been proved for strictly pseudoconvex domains. The atomic decomposition has also been proved for convex domains of finite type. Here the Hardy space was defined with respect to the ordinary Euclidean surface measure on the boundary. But for domains of finite type, it is natural to define $H^\{1\}$ with respect to a certain measure that degenerates near Levi-flat points and is closely related to explicit representation formulas for holomorphic functions. For the model domain $B^\{p\}=\big \lbrace z\in \{\Bbb C\}^\{n\}: \sum _\{j=1\}^\{n\}|z_\{j\}|^\{2p_\{j\}\}\le 1 \big \rbrace , p_\{j\}\in \{\Bbb Z\}^\{+\}$, both atomic decomposition and factorization of $H^\{1\}$-functions are established. The duality between $H^\{1\}$ and $BMOA$ is also considered.},
author = {Hansson, Thomas},
journal = {Annales de l'institut Fourier},
keywords = {Hardy spaces; atomic decomposition; factorization; complex ellipsoids},
language = {eng},
number = {5},
pages = {1477-1501},
publisher = {Association des Annales de l'Institut Fourier},
title = {On Hardy spaces in complex ellipsoids},
url = {http://eudml.org/doc/75391},
volume = {49},
year = {1999},
}

TY - JOUR
AU - Hansson, Thomas
TI - On Hardy spaces in complex ellipsoids
JO - Annales de l'institut Fourier
PY - 1999
PB - Association des Annales de l'Institut Fourier
VL - 49
IS - 5
SP - 1477
EP - 1501
AB - This paper deals with atomic decomposition and factorization of functions in the holomorphic Hardy space $H^{1}$. Such representation theorems have been proved for strictly pseudoconvex domains. The atomic decomposition has also been proved for convex domains of finite type. Here the Hardy space was defined with respect to the ordinary Euclidean surface measure on the boundary. But for domains of finite type, it is natural to define $H^{1}$ with respect to a certain measure that degenerates near Levi-flat points and is closely related to explicit representation formulas for holomorphic functions. For the model domain $B^{p}=\big \lbrace z\in {\Bbb C}^{n}: \sum _{j=1}^{n}|z_{j}|^{2p_{j}}\le 1 \big \rbrace , p_{j}\in {\Bbb Z}^{+}$, both atomic decomposition and factorization of $H^{1}$-functions are established. The duality between $H^{1}$ and $BMOA$ is also considered.
LA - eng
KW - Hardy spaces; atomic decomposition; factorization; complex ellipsoids
UR - http://eudml.org/doc/75391
ER -