Pluriharmonic functions on symmetric tube domains with BMO boundary values
Volume 94 / 2002
Colloquium Mathematicum 94 (2002), 67-86
MSC: 32M10, 32M15, 43A65, 43A80, 22E27.
DOI: 10.4064/cm94-1-6
Abstract
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.
