Pluriharmonic functions on symmetric tube domains with BMO boundary values

Ewa Damek, et al. "Pluriharmonic functions on symmetric tube domains with BMO boundary values." Colloquium Mathematicae 94.1 (2002): 67-86. <http://eudml.org/doc/285015>.

@article{EwaDamek2002,
abstract = {Let 𝓓 be a symmetric Siegel domain of tube type and S be a solvable Lie group acting simply transitively on 𝓓. Assume that L is a real S-invariant second order operator that satisfies Hörmander's condition and annihilates holomorphic functions. Let H be the Laplace-Beltrami operator for the product of upper half planes imbedded in 𝓓. We prove that if F is an L-Poisson integral of a BMO function and HF = 0 then F is pluriharmonic. Some other related results are also considered.},
author = {Ewa Damek, Jacek Dziubański, Andrzej Hulanicki, Jose L. Torrea},
journal = {Colloquium Mathematicae},
keywords = {pluriharmonic function; Siegel domain of tube type; invariant operator; BMO function},
language = {eng},
number = {1},
pages = {67-86},
title = {Pluriharmonic functions on symmetric tube domains with BMO boundary values},
url = {http://eudml.org/doc/285015},
volume = {94},
year = {2002},
}

TY - JOUR
AU - Ewa Damek
AU - Jacek Dziubański
AU - Andrzej Hulanicki
AU - Jose L. Torrea
TI - Pluriharmonic functions on symmetric tube domains with BMO boundary values
JO - Colloquium Mathematicae
PY - 2002
VL - 94
IS - 1
SP - 67
EP - 86
AB - Let 𝓓 be a symmetric Siegel domain of tube type and S be a solvable Lie group acting simply transitively on 𝓓. Assume that L is a real S-invariant second order operator that satisfies Hörmander's condition and annihilates holomorphic functions. Let H be the Laplace-Beltrami operator for the product of upper half planes imbedded in 𝓓. We prove that if F is an L-Poisson integral of a BMO function and HF = 0 then F is pluriharmonic. Some other related results are also considered.
LA - eng
KW - pluriharmonic function; Siegel domain of tube type; invariant operator; BMO function
UR - http://eudml.org/doc/285015
ER -