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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On the Bochner-Riesz means of critical order


Author: 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.


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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: http://dx.doi.org/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
Article copyright: © Copyright 1997 American Mathematical Society