Harmonic functions on the real hyperbolic ball I: Boundary values and atomic decomposition of Hardy spaces

Philippe Jaming

Colloquium Mathematicae (1999)

  • Volume: 80, Issue: 1, page 63-82
  • ISSN: 0010-1354

Abstract

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We study harmonic functions for the Laplace-eltrami operator on the real hyperbolic space n . We obtain necessary and sufficient conditions for these functions and their normal derivatives to have a boundary distribution. In doing so, we consider different behaviors of hyperbolic harmonic functions according to the parity of the dimension of the hyperbolic ball n . We then study the Hardy spaces H p ( n ) , 0

How to cite

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Jaming, Philippe. "Harmonic functions on the real hyperbolic ball I: Boundary values and atomic decomposition of Hardy spaces." Colloquium Mathematicae 80.1 (1999): 63-82. <http://eudml.org/doc/210706>.

@article{Jaming1999,
abstract = {We study harmonic functions for the Laplace-eltrami operator on the real hyperbolic space $_n$. We obtain necessary and sufficient conditions for these functions and their normal derivatives to have a boundary distribution. In doing so, we consider different behaviors of hyperbolic harmonic functions according to the parity of the dimension of the hyperbolic ball $_n$. We then study the Hardy spaces $H^p(_n)$, 0},
author = {Jaming, Philippe},
journal = {Colloquium Mathematicae},
keywords = {Hardy spaces; atomic decomposition; real hyperbolic ball; boundary values; harmonic functions; Laplace-Beltrami operator},
language = {eng},
number = {1},
pages = {63-82},
title = {Harmonic functions on the real hyperbolic ball I: Boundary values and atomic decomposition of Hardy spaces},
url = {http://eudml.org/doc/210706},
volume = {80},
year = {1999},
}

TY - JOUR
AU - Jaming, Philippe
TI - Harmonic functions on the real hyperbolic ball I: Boundary values and atomic decomposition of Hardy spaces
JO - Colloquium Mathematicae
PY - 1999
VL - 80
IS - 1
SP - 63
EP - 82
AB - We study harmonic functions for the Laplace-eltrami operator on the real hyperbolic space $_n$. We obtain necessary and sufficient conditions for these functions and their normal derivatives to have a boundary distribution. In doing so, we consider different behaviors of hyperbolic harmonic functions according to the parity of the dimension of the hyperbolic ball $_n$. We then study the Hardy spaces $H^p(_n)$, 0
LA - eng
KW - Hardy spaces; atomic decomposition; real hyperbolic ball; boundary values; harmonic functions; Laplace-Beltrami operator
UR - http://eudml.org/doc/210706
ER -

References

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  8. [8] P. Jaming, Trois problèmes d'analyse harmonique, PhD thesis, Université d'Orlé- ans, 1998. 
  9. [9] S. G. Krantz and S. Y. Li, On decomposition theorems for Hardy spaces on domains in ℂ n and applications, J. Fourier Anal. Appl. 2 (1995), 65-107. Zbl0886.32003
  10. [10] J. B. Lewis, Eigenfunctions on symmetric spaces with distribution-valued boundary forms, J. Funct. Anal. 29 (1978), 287-307. Zbl0398.43010
  11. [11] K. Minemura, Harmonic functions on real hyperbolic spaces, Hiroshima Math. J. 3 (1973), 121-151. Zbl0274.31004
  12. [12] K. Minemura, Eigenfunctions of the Laplacian on a real hyperbolic spaces, J. Math. Soc. Japan 27 (1975), 82-105. Zbl0292.35023
  13. [13] H. Samii, Les transformations de Poisson dans la boule hyperbolique, PhD thesis, Université Nancy 1, 1982. 
  14. [14] E. M. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton Univ. Press, 1970. Zbl0207.13501

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