Geodesic
Pluriharmonic functions on symmetric tube domains with BMO boundary values
Ewa Damek1 ; Jacek Dziubański2 ; Andrzej Hulanicki2 ; Jose L. Torrea3
1 Institute of Mathematics Wrocław University Pl. Grunwaldzki 2/4 50-384 Wrocław, Poland
2 Institute of Mathematics Wroclaw University Pl. Grunwaldzki 2/4 50-384 Wrocław, Poland
3 Departamento de Matemáticas Facultad de Ciencias Universidad Autónoma de Madrid 28049 Madrid, Spain
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.
DOI : 10.4064/cm94-1-6
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

Ewa Damek 1 ; Jacek Dziubański 2 ; Andrzej Hulanicki 2 ; Jose L. Torrea 3

1 Institute of Mathematics Wrocław University Pl. Grunwaldzki 2/4 50-384 Wrocław, Poland
2 Institute of Mathematics Wroclaw University Pl. Grunwaldzki 2/4 50-384 Wrocław, Poland
3 Departamento de Matemáticas Facultad de Ciencias Universidad Autónoma de Madrid 28049 Madrid, Spain 
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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. http://geodesic.mathdoc.fr/articles/10.4064/cm94-1-6/

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