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 Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In this note we improve, for the case of low dimensions, the known range ofexponents for which constant functions are the unique maximizers for the$L^2(\mathbb{S}^{d-1})$ to $L^p_{rad}L^2_{ang}(\mathbb{R}^d)$ mixed-normFourier extension estimate on the sphere. Moreover, we show that in the samerange of exponents for which constant functions are the unique maximizers forthe $L^2(\mathbb{S}^{d-1})$ to $L^p_{red}L^2_{ang}(\mathbb{R}^d)$ mixed-normFourier extension estimates they are also local maximizers for the$L^p(\mathbb{S}^{d-1})$ to $L^p(\mathbb{R}^d)$ Fourier extension estimates. Asa by-product, we obtain that for the cases of dimensions $d=2,3$ constantfunctions are local maximizers for all $p\geq p_{\mathrm{st}}(d)$, where$p_{\mathrm{st}}$ denotes the Stein-Tomas endpoint, $p_{\mathrm{st}}(d):=2(d+1)/(d-1)$.

Global and local maximizers for some Fourier extension estimates on the sphere