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

We estimate the Hopf degree for smooth maps $f$ from $\mathbb{S}^{4n-1}$ to$\mathbb{S}^{2n}$ in the fractional Sobolev space.  Namely we show that for $s \in [1 - \frac{1}{4n}, 1]$  \[  \left |{\rm deg}_H(f)\right | \lesssim[f]_{W^{s,\frac{4n-1}{s}}}^{\frac{4n}{s}}. \]  Our argument is based on the Whitehead integral formula and commutatorestimates for Jacobian-type expressions.

An estimate of the Hopf degree of fractional Sobolev mappings