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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.

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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