English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

In this paper, we will introduce and study several types of Kakeyainequalities by the maximal functions in Hardy spaces in $\RR^n$,\,$(n\geq2)$,and we could obtain several inequalities associated with the Kakeyainequalities. 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 $supp\,\hat{f}(\xi)\subseteq B(0,1)$.

Kakeya inequalities by maximal functions in Hardy spaces