Pluriharmonic functions on symmetric tube domains with BMO boundary values

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

Colloquium Mathematicum, Tome 94 (2002) no. 1, pp. 67-86

Résumé

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.

Détail

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