Proceedings of the American Mathematical Society

			Journals Home Search Author Info Subscribe Tech Support My Subscriptions Help
ISSN 1088-6826(e) ISSN 0002-9939(p)

Sharpness of the Korányi approach region

Author(s): Kentaro Hirata
Journal: Proc. Amer. Math. Soc. 133 (2005), 2309-2317.
MSC (2000): Primary 31B25, 31A20, 32A40
Posted: March 14, 2005
MathSciNet review: 2138873
Retrieve article in: PDF
This article is available free of charge

Abstract | References | Similar articles | Additional information

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).

References:

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)

Similar Articles:

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 31B25, 31A20, 32A40

Retrieve articles in all Journals with MSC (2000): 31B25, 31A20, 32A40

Additional Information:

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

DOI: 10.1090/S0002-9939-05-08020-2
PII: S 0002-9939(05)08020-2
Keywords: Poisson-Szeg\"o integral, Kor\'anyi's approach region, boundary behavior
Received by editor(s): September 17, 2003
Posted: March 14, 2005
Communicated by: Andreas Seeger
Copyright of article: Copyright 2005, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

	Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
\|