Pluriharmonic functions on symmetric tube domains with BMO boundary values

• Autorzy: Ewa Damek , Jacek Dziubański , Andrzej Hulanicki , Jose L. Torrea
• Języki publikacji: EN

Abstrakty

EN

Let 𝓓 be a symmetric Siegel domain of tube type and S be a solvable Lie group acting simply transitively on 𝓓. Assume that L is a real S-invariant second order operator that satisfies Hörmander's condition and annihilates holomorphic functions. Let H be the Laplace-Beltrami operator for the product of upper half planes imbedded in 𝓓. We prove that if F is an L-Poisson integral of a BMO function and HF = 0 then F is pluriharmonic. Some other related results are also considered.

Kategorie tematyczne

• 22E27: Representations of nilpotent and solvable Lie groups (special orbital integrals, non-type I representations, etc.)
• 43A80: Analysis on other specific Lie groups
• 43A65: Representations of groups, semigroups, etc.
• 32M10: Homogeneous complex manifolds
• 32M15: Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2002
• Tom: 94
• Numer: 1
• Strony: 67-86

Daty

wydano

2002

Twórcy

autor

Ewa Damek

• Institute of Mathematics, Wrocław University, Pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland

autor

Jacek Dziubański

• Institute of Mathematics, Wroclaw University, Pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland

autor

Andrzej Hulanicki

• Institute of Mathematics, Wroclaw University, Pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland

autor

Jose L. Torrea

• Departamento de Matemáticas, Facultad de Ciencias, Universidad Autónoma de Madrid, 28049 Madrid, Spain

Identyfikatory

DOI

10.4064/cm94-1-6