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Sharpness of the Korányi approach region


Author: Kentaro Hirata
Journal: Proc. Amer. Math. Soc. 133 (2005), 2309-2317
MSC (2000): Primary 31B25, 31A20, 32A40
DOI: https://doi.org/10.1090/S0002-9939-05-08020-2
Published electronically: March 14, 2005
MathSciNet review: 2138873
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Abstract: We prove a Littlewood-type theorem which shows the sharpness of the Korányi approach region for the boundary behavior of Poisson-Szegö integrals on the unit ball of $\mathbb{C} ^n$. Our result is stronger than Hakim and Sibony (1983).


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  • 1. H. Aikawa, Harmonic functions having no tangential limits, Proc. Amer. Math. Soc. 108 (1990), no. 2, 457-464. MR 0990410 (90h:31003)
  • 2. -, Harmonic functions and Green potentials having no tangential limits, J. London Math. Soc. (2), 43 (1991), no. 1, 125-136. MR 1099092 (92b:31005)
  • 3. M. Hakim and N. Sibony, Fonctions holomorphes bornées et limites tangentielles, Duke Math. J. 50 (1983), no. 1, 133-141. MR 0700133 (84m:32011)
  • 4. A. Korányi, Harmonic functions on Hermitian hyperbolic space, Trans. Amer. Math. Soc. 135 (1969), 507-516. MR 0277747 (43:3480)
  • 5. J. E. Littlewood, On a theorem of Fatou, J. London Math. Soc. 2 (1927), 172-176.
  • 6. A. Nagel and E. M. Stein, On certain maximal functions and approach regions, Adv. in Math. 54 (1984), 83-106. MR 0761764 (86a:42026)
  • 7. M. Stoll, Invariant potential theory in the unit ball of $C\sp n$, London Mathematical Society Lecture Note Series, 199. Cambridge University Press, Cambridge, 1994. MR 1297545 (96f:31011)
  • 8. J. Sueiro, On maximal functions and Poisson-Szegö integrals, Trans. Amer. Math. Soc. 298 (1986), no. 2, 653-669. MR 0860386 (87m:42017)

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Additional Information

Kentaro Hirata
Affiliation: Department of Mathematics, Shimane University, Matsue 690-8504, Japan
Email: hirata@math.shimane-u.ac.jp

DOI: https://doi.org/10.1090/S0002-9939-05-08020-2
Keywords: Poisson-Szeg\"o integral, Kor\'anyi's approach region, boundary behavior
Received by editor(s): September 17, 2003
Published electronically: March 14, 2005
Communicated by: Andreas Seeger
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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