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 Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

In this article, we introduce anisotropic mixed-norm Herz spacesK˙q→,a→α,p(Rn){\dot{K}}_{\overrightarrow{q},\overrightarrow{a}}^{\alpha ,p}\left({{\mathbb{R}}}^{n})andKq→,a→α,p(Rn){K}_{\overrightarrow{q},\overrightarrow{a}}^{\alpha ,p}\left({{\mathbb{R}}}^{n})and investigate some basic properties of those spaces. Furthermore, we establish the Rubio de Francia extrapolation theory, which resolves the boundedness problems of Calderón-Zygmund operators and fractional integral operator and their commutators, on spacesK˙q→,a→α,p(Rn){\dot{K}}_{\overrightarrow{q},\overrightarrow{a}}^{\alpha ,p}\left({{\mathbb{R}}}^{n})andKq→,a→α,p(Rn){K}_{\overrightarrow{q},\overrightarrow{a}}^{\alpha ,p}\left({{\mathbb{R}}}^{n}). Especially, the Littlewood-Paley characterizations of anisotropic mixed-norm Herz spaces are also gained. As the generalization of anisotropic mixed-norm Herz spaces, we introduce anisotropic mixed-norm Herz-Hardy spacesHK˙q→,a→α,p(Rn)H{\dot{K}}_{\overrightarrow{q},\overrightarrow{a}}^{\alpha ,p}\left({{\mathbb{R}}}^{n})andHKq→,a→α,p(Rn)H{K}_{\overrightarrow{q},\overrightarrow{a}}^{\alpha ,p}\left({{\mathbb{R}}}^{n}), on which atomic decomposition and molecular decomposition are obtained. Moreover, we gain the boundedness of classical Calderón-Zygmund operators.

Hardy spaces associated with some anisotropic mixed-norm Herz spaces and their applications