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 study different types of weighted Besov andTriebel-Lizorkin spaces with variable smoothness. The function spaces can bedefined by means of the Littlewood-Paley theory in the field of Fourieranalysis, while there are other norms arising in the theory of partialdifferential equations such as Sobolev-Slobodeckij spaces. It is known that twonorms are equivalent when one considers constant regularity function spaceswithout weights. We show that the equivalence still holds for variablesmoothness and weights, which is accomplished by making use of shifted maximalfunctions, Peetre's maximal functions, and the reverse H\"older inequality.Moreover, we obtain a weighted regularity estimate for time-fractionalevolution equations and a generalized Sobolev embedding theorem withoutweights.

Characterizations of weighted Besov and Triebel-Lizorkin spaces with variable smoothness