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

Chen, Lung-Kee; Fan, Dashan

doi:10.1090/S0002-9939-96-03333-3

The convergence of the Bochner-Riesz means at the critical index
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by Lung-Kee Chen and Dashan Fan

Proc. Amer. Math. Soc. 124 (1996), 2717-2726

DOI: https://doi.org/10.1090/S0002-9939-96-03333-3

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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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