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:
https://doi.org/10.1090/S0002-9939-97-03742-8

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