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

If $f:{\bf R}^d\to{\bf C}$ is bounded and $f$'s H\"older $\alpha$-modulus ofcontinuity grows no faster than $(1+\vert x\vert)^M$ ($M\geq0$) then, for every$\epsilon>0$, there is a $\beta>0$ such that $f$'s H\"older $\beta$-modulusgrows no faster than $(1+\vert x\vert)^{\epsilon}$. We use this easy fact toshow that, if $\vert f\vert$ decays as fast as $(1+\vert x\vert)^{-R}$ (for$R>0$) and $f$'s $\alpha$-H\"older modulus grows no faster than $(1+\vertx\vert)^M$, then, for every $0\leq R'< R$, there is a $\beta>0$ such that $f$'s$\beta$-H\"older modulus decays as fast as $(1+\vert x\vert)^{-R'}$. We applythis to strengthen a result of Coifman and Meyer on almost-orthogonality ofvaguelet families and to derive other useful facts about vaguelets andvaguelet-like functions.

Growth and decay of H\"older moduli