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 the class of Muckenhoupt A_p weights coincides with theintersection of finitely many suitable translates of dyadic A_p, in both theone-parameter and multiparameter cases, and that the analogous results hold forthe reverse H\"older class RH_p, for doubling measures, and for the space VMOof functions of vanishing mean oscillation. We extend to the multiparameter(product) space BMO of functions of bounded mean oscillation the correspondingone-parameter BMO result due to T. Mei, by means of the Carleson-measurecharacterization of multiparameter BMO. Our results hold in both the compactand non-compact cases. In addition, we survey several definitions of VMO andprove their equivalences, in the continuous, dyadic, one-parameter andmultiparameter cases. We show that the weighted Hardy space H^1(\omega) is thesum of finitely many suitable translates of dyadic weighted H^1(\omega), andthat the weighted maximal function is pointwise comparable to the sum offinitely many dyadic weighted maximal functions for suitable translates of thedyadic grid and for each doubling weight \omega.

One-parameter and multiparameter function classes are intersections of finitely many dyadic classes