On pointwise convergence of sequential Boussinesq operator

Dan Li; Fangyuan Chen; Dan Li; Fangyuan Chen

doi:10.3934/math.20241086

AIMS Mathematics

2024, Volume 9, Issue 8: 22301-22320. doi: 10.3934/math.20241086

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On pointwise convergence of sequential Boussinesq operator

Dan Li ¹,
Fangyuan Chen ^{2
,
,}

1.
School of Mathematics and Statistics, Beijing Technology and Business University, Beijing 100048, China
2.
School of Arts and Sciences, Beijing Institute of Fashion Technology, Beijing, 100029, China

Received: 21 February 2024 Revised: 12 June 2024 Accepted: 12 July 2024 Published: 17 July 2024
MSC : 42B25, 35Q41

We study the almost everywhere pointwise convergence of the Boussinesq operator along sequences $ \{t_n\}_{n = 1}^\infty $ with $ \lim\limits_{n\rightarrow \infty} t_n = 0 $ in one dimension. We obtain a characterization of convergence almost everywhere when $ \{t_n\}\in l^{r, \infty}(\mathbb{N}) $ for all $ f\in H^s(\mathbb{R}) $ provided $ 0 < s < \frac12 $.
- Boussinesq operator,
- pointwise convergence,
- Sobolev space,
- Lorentz space
Citation: Dan Li, Fangyuan Chen. On pointwise convergence of sequential Boussinesq operator[J]. AIMS Mathematics, 2024, 9(8): 22301-22320. doi: 10.3934/math.20241086

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Abstract

We study the almost everywhere pointwise convergence of the Boussinesq operator along sequences $ \{t_n\}_{n = 1}^\infty $ with $ \lim\limits_{n\rightarrow \infty} t_n = 0 $ in one dimension. We obtain a characterization of convergence almost everywhere when $ \{t_n\}\in l^{r, \infty}(\mathbb{N}) $ for all $ f\in H^s(\mathbb{R}) $ provided $ 0 < s < \frac12 $.

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