Sharpness of the Korányi approach region
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- by Kentaro Hirata PDF
- Proc. Amer. Math. Soc. 133 (2005), 2309-2317 Request permission
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
- Hiroaki Aikawa, Harmonic functions having no tangential limits, Proc. Amer. Math. Soc. 108 (1990), no. 2, 457–464. MR 990410, DOI 10.1090/S0002-9939-1990-0990410-X
- Hiroaki Aikawa, Harmonic functions and Green potentials having no tangential limits, J. London Math. Soc. (2) 43 (1991), no. 1, 125–136. MR 1099092, DOI 10.1112/jlms/s2-43.1.125
- Monique Hakim and Nessim Sibony, Fonctions holomorphes bornées et limites tangentielles, Duke Math. J. 50 (1983), no. 1, 133–141 (French). MR 700133
- Adam Korányi, Harmonic functions on Hermitian hyperbolic space, Trans. Amer. Math. Soc. 135 (1969), 507–516. MR 277747, DOI 10.1090/S0002-9947-1969-0277747-0
- J. E. Littlewood, On a theorem of Fatou, J. London Math. Soc. 2 (1927), 172–176.
- Alexander Nagel and Elias M. Stein, On certain maximal functions and approach regions, Adv. in Math. 54 (1984), no. 1, 83–106. MR 761764, DOI 10.1016/0001-8708(84)90038-0
- Manfred Stoll, Invariant potential theory in the unit ball of $\textbf {C}^n$, London Mathematical Society Lecture Note Series, vol. 199, Cambridge University Press, Cambridge, 1994. MR 1297545, DOI 10.1017/CBO9780511526183
- Juan Sueiro, On maximal functions and Poisson-Szegő integrals, Trans. Amer. Math. Soc. 298 (1986), no. 2, 653–669. MR 860386, DOI 10.1090/S0002-9947-1986-0860386-8
Additional Information
- Kentaro Hirata
- Affiliation: Department of Mathematics, Shimane University, Matsue 690-8504, Japan
- Email: hirata@math.shimane-u.ac.jp
- Received by editor(s): September 17, 2003
- Published electronically: March 14, 2005
- Communicated by: Andreas Seeger
- © Copyright 2005
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - 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
- MathSciNet review: 2138873