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On the Bochner-Riesz means of critical order
Author(s):
E.
R.
Liflyand
Journal:
Proc. Amer. Math. Soc.
125
(1997),
1443-1450.
MSC (1991):
Primary 42A24
MathSciNet review:
1371133
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Abstract:
Stein's well-known logarithmic asymptotics of the Lebesgue constants of the Bochner-Riesz means of critical order is extended to Lebesgue constants of more general linear means of multiple Fourier series. These means are generated by certain class of functions supported in convex domains with boundaries of non-vanishing Gaussian curvature.
References:
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- [Bc]
- S. Bochner, Summation of multiple Fourier series by spherical means, Trans. Amer. Math. Soc. 40 (1936), 175 - 207.
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- E. S. Belinskii, Behavior of Lebesgue constants for some methods of summation of multiple Fourier series, Metric Questions in the Theory of Functions and Mappings, Naukova Dumka, Kiev, 1977, pp. (19 - 39) (Russian). MR 58:29816
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 norms of certain kernels of the  -dimensional torus, Trans. Amer. Math. Soc 266 (2) (1981), 617 - 627. MR 84e:42008 - [Gi]
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- [LRZ]
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- -, Asymptotic behavior of the Fourier transform of piecewise-smooth functions, C. R. Acad. Sci. Paris 316 (6) (1993), 541-546. MR 94d:42019
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Additional Information:
E.
R.
Liflyand
Affiliation:
Department of Mathematics and Computer Science, Bar Ilan University, Ramat Gan, 52900, Israel
Email:
liflyand@bimacs.cs.biu.ac.il
DOI:
10.1090/S0002-9939-97-03742-8
PII:
S 0002-9939(97)03742-8
Keywords:
Lebesgue constants,
Bochner-Riesz means,
critical order
Received by editor(s):
January 4, 1994
Received by editor(s) in revised form:
November 27, 1995
Additional Notes:
The author acknowledges the support of the Minerva Foundation in Germany through the Emmy Noether Institute in Bar-Ilan University.
Communicated by:
J. Marshall Ash
Copyright of article:
Copyright
1997,
American Mathematical Society
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