Invariant operators and pluriharmonic functions on symmetric irreducible Siegel domains

Ewa Damek; Andrzej Hulanicki

Studia Mathematica (2000)

  • Volume: 139, Issue: 2, page 101-140
  • ISSN: 0039-3223

Abstract

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Let D be a symmetric irreducible Siegel domain. Pluriharmonic functions satisfying a certain rather weak growth condition are characterized by r+2 operators (r+1 in the tube case), r being the rank of the underlying symmetric cone

How to cite

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Damek, Ewa, and Hulanicki, Andrzej. "Invariant operators and pluriharmonic functions on symmetric irreducible Siegel domains." Studia Mathematica 139.2 (2000): 101-140. <http://eudml.org/doc/216715>.

@article{Damek2000,
abstract = {Let D be a symmetric irreducible Siegel domain. Pluriharmonic functions satisfying a certain rather weak growth condition are characterized by r+2 operators (r+1 in the tube case), r being the rank of the underlying symmetric cone},
author = {Damek, Ewa, Hulanicki, Andrzej},
journal = {Studia Mathematica},
keywords = {pluriharmonic functions; symmetric irreducible Siegel domain},
language = {eng},
number = {2},
pages = {101-140},
title = {Invariant operators and pluriharmonic functions on symmetric irreducible Siegel domains},
url = {http://eudml.org/doc/216715},
volume = {139},
year = {2000},
}

TY - JOUR
AU - Damek, Ewa
AU - Hulanicki, Andrzej
TI - Invariant operators and pluriharmonic functions on symmetric irreducible Siegel domains
JO - Studia Mathematica
PY - 2000
VL - 139
IS - 2
SP - 101
EP - 140
AB - Let D be a symmetric irreducible Siegel domain. Pluriharmonic functions satisfying a certain rather weak growth condition are characterized by r+2 operators (r+1 in the tube case), r being the rank of the underlying symmetric cone
LA - eng
KW - pluriharmonic functions; symmetric irreducible Siegel domain
UR - http://eudml.org/doc/216715
ER -

References

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  2. [D] E. Damek, Left-invariant degenerate elliptic operators on semidirect extensions of homogeneous groups, Studia Math. 89 (1988), 169-196. Zbl0675.22005
  3. [DH] E. Damek and A. Hulanicki, Boundaries for left-invariant subelliptic operators on semidirect products of nilpotent and abelian groups, J. Reine Angew. Math. 411 (1990), 1-38. Zbl0699.22012
  4. [DHMP] E. Damek, A. Hulanicki, D. Müller and M. Peloso, Pluriharmonic H 2 functions on symmetric irreducible Siegel domains, Geom. Funct. Anal., to appear. Zbl0969.31007
  5. [DHP] E. Damek, A. Hulanicki and R. Penney, Hua operators on bounded homogeneous domains in ℂ n and alternative reproducing kernels for holomorphic functions, J. Funct. Anal. 151 (1997), 77-120. Zbl0887.43005
  6. [FK] J. Faraut and A. Korányi, Analysis on Symmetric Cones, Oxford Math. Monographs, Oxford Sci. Publ., Clarendon Press, 1994. Zbl0841.43002
  7. [F] F. Forelli, Pluriharmonicity in terms of harmonic slices, Math. Scand. 41 (1977), 358-364. Zbl0373.31006
  8. [KW] A. Korányi and J. Wolf, Realization of hermitian symmetric spaces as generalized half-planes, Ann. of Math. (2) 81 (1965), 265-288. Zbl0137.27402
  9. [K] J. L. Koszul, Sur la forme hermitienne canonique des espaces homogènes complexes, Canad. J. Math. 7 (1955), 562-576. Zbl0066.16104
  10. [L1] G. Laville, Fonctions pluriharmoniques et solution fondamentale d’un opérateur du 4 e ordre, Bull. Sci. Math. 101 (1977), 305-317. Zbl0397.35021
  11. [L2] G. Laville, Sur le calcul de la fonction conjuguée à plusieurs variables complexes, ibid. 102 (1978), 257-272. Zbl0396.35017
  12. [OV] R. D. Ogden and S. Vági, Harmonic analysis of a nilpotent group and function theory on Siegel domains of type II, Adv. in Math. 33 (1979), 31-92. Zbl0463.43002

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