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arXiv · 2004.01775

Kakeya inequalities by maximal functions in Hardy spaces

Zhuo Ran Hu
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Abstract

In this paper, we will introduce and study several types of Kakeya inequalities by the maximal functions in Hardy spaces in $\RR^n$,\,$(n\geq2)$, and we could obtain several inequalities associated with the Kakeya inequalities. We will show that $\big\|M^t_{\delta S_{\alpha,\beta}} f \big\|_p\lesssim_{p,n,\varphi,\varepsilon}\left(\frac{1}{\delta}\right)^{5\left(\frac{n}{r}+2\right)\varepsilon}\big\|f\big\|_p$, when $f(x)\in L^p(\RR^n)$ and $supp\,\hat{f}(\xi)\subseteq B(0,1)$.

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Zhuo Ran Hu. 2020-03-18. Kakeya inequalities by maximal functions in Hardy spaces. https://doi.org/10.1155/2022/9821212

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