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ArticleOriginal scientific text

Title

Invariant operators and pluriharmonic functions on symmetric irreducible Siegel domains

Authors 1, 1

Affiliations

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

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

Bibliography

  1. [BBG] A. Bonami, J. Bruna and S. Grellier, On Hardy, BMO and Lipschitz spaces of invariantly harmonic functions in the unit ball, Proc. London Math. Soc. 77 (1998), 665-696.
  2. [D] E. Damek, Left-invariant degenerate elliptic operators on semidirect extensions of homogeneous groups, Studia Math. 89 (1988), 169-196.
  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.
  4. [DHMP] E. Damek, A. Hulanicki, D. Müller and M. Peloso, Pluriharmonic H2 functions on symmetric irreducible Siegel domains, Geom. Funct. Anal., to appear.
  5. [DHP] E. Damek, A. Hulanicki and R. Penney, Hua operators on bounded homogeneous domains in ℂn and alternative reproducing kernels for holomorphic functions, J. Funct. Anal. 151 (1997), 77-120.
  6. [FK] J. Faraut and A. Korányi, Analysis on Symmetric Cones, Oxford Math. Monographs, Oxford Sci. Publ., Clarendon Press, 1994.
  7. [F] F. Forelli, Pluriharmonicity in terms of harmonic slices, Math. Scand. 41 (1977), 358-364.
  8. [KW] A. Korányi and J. Wolf, Realization of hermitian symmetric spaces as generalized half-planes, Ann. of Math. (2) 81 (1965), 265-288.
  9. [K] J. L. Koszul, Sur la forme hermitienne canonique des espaces homogènes complexes, Canad. J. Math. 7 (1955), 562-576.
  10. [L1] G. Laville, Fonctions pluriharmoniques et solution fondamentale d'un opérateur du 4e ordre, Bull. Sci. Math. 101 (1977), 305-317.
  11. [L2] G. Laville, Sur le calcul de la fonction conjuguée à plusieurs variables complexes, ibid. 102 (1978), 257-272.
  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.
Studia Mathematica
2000/139/2
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Pages:
101-140
Main language of publication
English
Received
1999-01-04
Published
2000
Exact and natural sciences