Page 1

Displaying 1 – 17 of 17

Showing per page

Pluriharmonic functions on symmetric tube domains with BMO boundary values

Ewa Damek, Jacek Dziubański, Andrzej Hulanicki, Jose L. Torrea (2002)

Colloquium Mathematicae

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.

Polynomially growing pluriharmonic functions on Siegel domains

Monika Gilżyńska (2007)

Colloquium Mathematicae

Let 𝓓 be a symmetric type two Siegel domain over the cone of positive definite Hermitian matrices and let N(Φ)S be a solvable Lie group acting simply transitively on 𝓓. We characterize polynomially growing pluriharmonic functions on 𝓓 by means of three N(Φ)S-invariant second order elliptic degenerate operators.

Currently displaying 1 – 17 of 17

Page 1