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

We prove that in a metric measure space $(X, d, \mu)$, the averagingoperators $A_{r, \mu }$ satisfy a uniform strong type $(1,1)$ bound $\sup_{r,\mu} \|A_{r, \mu }\|_{L^1\to L^1} < \infty$ if and only if $X$ satisfies acertain geometric condition, the equal radius Besicovitch intersectionproperty.

A characterization of the uniform strong type $(1,1)$ bounds for averaging operators