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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm94-1-6,
author = {Ewa Damek and Jacek Dziuba\'nski and Andrzej Hulanicki and Jose L. Torrea},
title = {Pluriharmonic functions on symmetric tube domains with BMO boundary values},
journal = {Colloquium Mathematicae},
volume = {91},
year = {2002},
pages = {67-86},
zbl = {1029.32008},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm94-1-6}
}
Ewa Damek; Jacek Dziubański; Andrzej Hulanicki; Jose L. Torrea. Pluriharmonic functions on symmetric tube domains with BMO boundary values. Colloquium Mathematicae, Tome 91 (2002) pp. 67-86. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm94-1-6/