Kakeya inequalities by maximal functions in Hardy spaces
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 $\big\|M^t_{δS_{α,β}} f \big\|_p\lesssim_{p,n,φ,\varepsilon}\left(\frac{1}δ\right)^{5\left(\frac{n}{r}+2\right)\varepsilon}\big\|f\big\|_p$, when $f(x)\in L^p(\RR^n)$ and $supp\,\hat{f}(ξ)\subseteq B(0,1)$.
math.CA↗