JEDNOSTKA NAUKOWA KATEGORII A+

Pluriharmonic functions on symmetric tube domains with BMO boundary values

Tom 94 / 2002

Ewa Damek, Jacek Dziubański, Andrzej Hulanicki, Jose L. Torrea 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
    Facultad de Ciencias
    Universidad Autónoma de Madrid
    28049 Madrid, Spain
    e-mail

Przeszukaj wydawnictwa IMPAN

Zbyt krótkie zapytanie. Wpisz co najmniej 4 znaki.

Przepisz kod z obrazka

Odśwież obrazek

Odśwież obrazek