Pluriharmonic functions on symmetric tube domains
with BMO boundary values
Colloquium Mathematicum, Tome 94 (2002) no. 1, pp. 67-86
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
Let ${\cal D}$ be a symmetric Siegel domain of tube type and $S$ be a solvable Lie group acting simply transitively on ${\cal D}$. Assume that $L$ is a real $S$-invariant second order operator that satisfies Hörmander's condition and annihilates holomorphic functions. Let ${\bf H}$ be the Laplace–Beltrami operator for the product of upper half planes imbedded in ${\cal D}$. We prove that if $F$ is an $L$-Poisson integral of a BMO function and ${\bf H}F=0$ then $F$ is pluriharmonic. Some other related results are also considered.
Keywords:
cal symmetric siegel domain tube type solvable lie group acting simply transitively cal assume real s invariant second order operator satisfies rmanders condition annihilates holomorphic functions laplace beltrami operator product upper half planes imbedded cal prove l poisson integral bmo function pluriharmonic other related results considered
Affiliations des auteurs :
Ewa Damek 1 ; Jacek Dziubański 2 ; Andrzej Hulanicki 2 ; Jose L. Torrea 3
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author = {Ewa Damek and Jacek Dziuba\'nski and Andrzej Hulanicki and Jose L. Torrea},
title = {Pluriharmonic functions on symmetric tube domains
with {BMO} boundary values},
journal = {Colloquium Mathematicum},
pages = {67--86},
publisher = {mathdoc},
volume = {94},
number = {1},
year = {2002},
doi = {10.4064/cm94-1-6},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/cm94-1-6/}
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Ewa Damek; Jacek Dziubański; Andrzej Hulanicki; Jose L. Torrea. Pluriharmonic functions on symmetric tube domains with BMO boundary values. Colloquium Mathematicum, Tome 94 (2002) no. 1, pp. 67-86. doi: 10.4064/cm94-1-6
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