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# Wydawnictwa / Czasopisma IMPAN / Colloquium Mathematicum / Wszystkie zeszyty

## Pluriharmonic functions on symmetric tube domains with BMO boundary values

### Tom 94 / 2002

Colloquium Mathematicum 94 (2002), 67-86 MSC: 32M10, 32M15, 43A65, 43A80, 22E27. DOI: 10.4064/cm94-1-6

#### Streszczenie

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.

#### Autorzy

• Ewa DamekInstitute of Mathematics
Wrocław University
Pl. Grunwaldzki 2/4
50-384 Wrocław, Poland
e-mail
• Jacek DziubańskiInstitute of Mathematics
Wroclaw University
Pl. Grunwaldzki 2/4
50-384 Wrocław, Poland
e-mail
• Andrzej HulanickiInstitute of Mathematics
Wroclaw University
Pl. Grunwaldzki 2/4
50-384 Wrocław, Poland
e-mail
• Jose L. TorreaDepartamento de Matemáticas