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 $.
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
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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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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