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 paper, we establish the equivalence between the Haj{\l}asz-Sobolevspaces or classical Triebel-Lizorkin spaces and a class of grandTriebel-Lizorkin spaces on Euclidean spaces and also on metric spaces that areboth doubling and reverse doubling. In particular, when $p\in(n/(n+1),\infty)$,we give a new characterization of the Haj{\l}asz-Sobolev spaces $\dot M^{1,p}({\mathbb R}^n)$ via a grand Littlewood-Paley function.

A Characterization of Haj{\l}asz-Sobolev and Triebel-Lizorkin Spaces via Grand Littlewood-Paley Functions