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Research Article | Open Access

On pointwise convergence of sequential Boussinesq operator

Dan Li1, Fangyuan Chen2( )
School of Mathematics and Statistics, Beijing Technology and Business University, Beijing 100048, China
School of Arts and Sciences, Beijing Institute of Fashion Technology, Beijing, 100029, China
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Abstract

We study the almost everywhere pointwise convergence of the Boussinesq operator along sequences {tn}n=1∞ with limn→∞tn=0 in one dimension. We obtain a characterization of convergence almost everywhere when {tn}∈lr,∞(N) for all f∈Hs(R) provided 0<s<12.

Keywords

Boussinesq operatorpointwise convergenceSobolev spaceLorentz space
CLC number: 42B25, 35Q41

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AIMS Mathematics
Volume 9 Issue 8,
August 2024
Pages 22301-22320
DOI: 10.3934/math.20241086

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Li D, Chen F. On pointwise convergence of sequential Boussinesq operator. AIMS Mathematics, 2024, 9(8): 22301-22320. https://doi.org/10.3934/math.20241086

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Received: 21 February 2024
Revised: 12 June 2024
Accepted: 12 July 2024
Published: 15 August 2024
©2024 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)