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The convergence of the Bochner-Riesz
means at the critical index

Authors: Lung-Kee Chen and Dashan Fan
Journal: Proc. Amer. Math. Soc. 124 (1996), 2717-2726
MSC (1991): Primary 42A20, 42B05
MathSciNet review: 1327002
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Abstract: In this paper, we study the pointwise convergence of the Bochner-Riesz means at the critical index on the space $L\log ^+ L (Q_n).$ We weaken the hypothesis, $`` x$ is a Lebesgue point", which is required on some research results by instead considering the convergence of averages of the function over balls when the radials of the balls approach to 0.

References [Enhancements On Off] (What's this?)

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Additional Information

Lung-Kee Chen
Affiliation: Department of Mathematics, Oregon State University, Corvallis, Oregon 97331

Dashan Fan
Affiliation: Department of Mathematical Sciences, University of Wisconsin-Milwaukee, Milwaukee, Wisconsin 53201

Received by editor(s): August 9, 1994
Received by editor(s) in revised form: February 28, 1995
Additional Notes: The second author was supported in part by a grant of the graduate school research committee in the University of Wisconsin-Milwaukee.
Communicated by: J. Marshall Ash
Article copyright: © Copyright 1996 American Mathematical Society