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February 2019 The rate of almost-everywhere convergence of Bochner–Riesz means on Sobolev spaces
Junyan Zhao, Dashan Fan
Ann. Funct. Anal. 10(1): 29-45 (February 2019). DOI: 10.1215/20088752-2018-0006

Abstract

We investigate the convergence rate of the generalized Bochner–Riesz means SRδ,γ on Lp-Sobolev spaces in the sharp range of δ and p (p2). We give the relation between the smoothness imposed on functions and the rate of almost-everywhere convergence of SRδ,γ. As an application, the corresponding results can be extended to the n-torus Tn by using some transference theorems. Also, we consider the following two generalized Bochner–Riesz multipliers, (1|ξ|γ1)+δ and (1|ξ|γ2)+δ, where γ1, γ2, δ are positive real numbers. We prove that, as the maximal operators of the multiplier operators with respect to the two functions, their L2(|x|β)-boundedness is equivalent for any γ1, γ2 and fixed δ.

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Junyan Zhao. Dashan Fan. "The rate of almost-everywhere convergence of Bochner–Riesz means on Sobolev spaces." Ann. Funct. Anal. 10 (1) 29 - 45, February 2019. https://doi.org/10.1215/20088752-2018-0006

Information

Received: 3 November 2017; Accepted: 11 February 2018; Published: February 2019
First available in Project Euclid: 16 January 2019

zbMATH: 07045483
MathSciNet: MR3899954
Digital Object Identifier: 10.1215/20088752-2018-0006

Subjects:
Primary: 42B15
Secondary: 41A35, 46E35, 47B38

Rights: Copyright © 2019 Tusi Mathematical Research Group

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Vol.10 • No. 1 • February 2019
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