Poisson-like kernels in tube domains over light-cones

Gustavo Garrigós

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (2002)

  • Volume: 13, Issue: 3-4, page 271-283
  • ISSN: 1120-6330

Abstract

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A family of holomorphic function spaces can be defined with reproducing kernels B α ⁢ z , w , obtained as real powers of the Cauchy-Szegö kernel. In this paper we study properties of the associated Poisson-like kernels: P α ⁢ z , w = B α ⁢ z , w 2 / B α ⁢ z , z . In particular, we show boundedness of associated maximal operators, and obtain formulas for the limit of Poisson integrals in the topological boundary of the cone.

How to cite

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Garrigós, Gustavo. "Poisson-like kernels in tube domains over light-cones." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 13.3-4 (2002): 271-283. <http://eudml.org/doc/252405>.

@article{Garrigós2002,
abstract = {A family of holomorphic function spaces can be defined with reproducing kernels $B_\{\alpha\}(z,w)$, obtained as real powers of the Cauchy-Szegö kernel. In this paper we study properties of the associated Poisson-like kernels: $P_\{\alpha\}(z,w) = |B_\{\alpha\}(z,w)|^\{2\} / B_\{\alpha\}(z,z)$. In particular, we show boundedness of associated maximal operators, and obtain formulas for the limit of Poisson integrals in the topological boundary of the cone.},
author = {Garrigós, Gustavo},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Tube domain; Poisson kernel; Maximal function; Bergman space; tube domain; maximal function; Bergmann space},
language = {eng},
month = {12},
number = {3-4},
pages = {271-283},
publisher = {Accademia Nazionale dei Lincei},
title = {Poisson-like kernels in tube domains over light-cones},
url = {http://eudml.org/doc/252405},
volume = {13},
year = {2002},
}

TY - JOUR
AU - Garrigós, Gustavo
TI - Poisson-like kernels in tube domains over light-cones
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 2002/12//
PB - Accademia Nazionale dei Lincei
VL - 13
IS - 3-4
SP - 271
EP - 283
AB - A family of holomorphic function spaces can be defined with reproducing kernels $B_{\alpha}(z,w)$, obtained as real powers of the Cauchy-Szegö kernel. In this paper we study properties of the associated Poisson-like kernels: $P_{\alpha}(z,w) = |B_{\alpha}(z,w)|^{2} / B_{\alpha}(z,z)$. In particular, we show boundedness of associated maximal operators, and obtain formulas for the limit of Poisson integrals in the topological boundary of the cone.
LA - eng
KW - Tube domain; Poisson kernel; Maximal function; Bergman space; tube domain; maximal function; Bergmann space
UR - http://eudml.org/doc/252405
ER -

References

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  10. Stein, E., Some problems in harmonic analysis suggested by symmetric spaces and semi-simple Lie groups. Actes, Congrès intern. math.1, 1970, 173-189. Zbl0252.43022MR578903
  11. Stein, E., Harmonic Analysis. Princeton University Press, 1993. Zbl0821.42001MR1232192
  12. Stein, E. - Weiss, G., Fourier Analysis on Euclidean Spaces. Princeton University Press, 1971. Zbl0232.42007MR304972
  13. Stein, E. - Weiss, G. - Weiss, M., H p classes of holomorphic functions in tube domains. Proc. Nat. Acad. Sci. USA, 52, 1964, 1035-1039. Zbl0126.09405MR179386
  14. Vergne, M. - Rossi, H., Analytic continuation of the holomorphic discrete series of a semi-simple Lie group. Acta Math., 136, 1976, 1-59. Zbl0356.32020MR480883

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