Triebel-Lizorkin space, singular kernels, generalized Marcinkiewicz integrals, $ L^p $ estimates, extrapolation

Autor: Dan Li, Fangyuan Chen
Jazyk: angličtina
Rok vydání: 2024
Předmět:
Zdroj: AIMS Mathematics, Vol 9, Iss 8, Pp 22301-22320 (2024)
Druh dokumentu: article
ISSN: 2473-6988
DOI: 10.3934/math.20241086?viewType=HTML
Popis: 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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