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

Let $p\in[1,\infty]$, $q\in(1,\infty)$,$s\in\mathbb{Z}_+:=\mathbb{N}\cup\{0\}$, and $\alpha\in\mathbb{R}$. In thisarticle, the authors introduce a reasonable version $\widetilde T$ of theCalder\'on--Zygmund operator $T$ on$JN_{(p,q,s)_\alpha}^{\mathrm{con}}(\mathbb{R}^n)$, the specialJohn--Nirenberg--Campanato space via congruent cubes, which coincides with theCampanato space $\mathcal{C}_{\alpha,q,s}(\mathbb{R}^n)$ when $p=\infty$. Thenthe authors prove that $\widetilde T$ is bounded on$JN_{(p,q,s)_\alpha}^{\mathrm{con}}(\mathbb{R}^n)$ if and only if, for any$\gamma\in\mathbb{Z}_+^n$ with $|\gamma|\leq s$, $T^*(x^{\gamma})=0$, which isa well-known assumption. To this end, the authors find an equivalent version ofthis assumption. Moreover, the authors show that $T$ can be extended to aunique continuous linear operator on the Hardy-kind space$HK_{(p,q,s)_{\alpha}}^{\mathrm{con}}(\mathbb{R}^n)$, the predual space of$JN_{(p',q',s)_\alpha}^{\mathrm{con}}(\mathbb{R}^n)$ with$\frac{1}{p}+\frac{1}{p'}=1=\frac{1}{q}+\frac{1}{q'}$, if and only if, for any$\gamma\in\mathbb{Z}_+^n$ with $|\gamma|\leq s$, $T^*(x^{\gamma})=0$.

Boundedness of Calder\'on--Zygmund Operators on Special John--Nirenberg--Campanato and Hardy-Type Spaces via Congruent Cubes