Localized John–Nirenberg–Campanato spaces

Let $$p\in (1,\infty )$$ , $$q\in [1,\infty $$s\in {\mathbb Z}_{+}$$ $$\alpha \in [0,\infty and $$\mathcal {X}$$ be $$\mathbb R^n$$ or a cube $$Q_0\subsetneqq \mathbb . In this article, the authors first introduce local John–Nirenberg–Campanato space $$jn_{(p,q,s)_{\alpha }}(\mathcal {X})$$ show that localized Campanato is limit case of as $$p\rightarrow \infty $$ By means atoms weak- $$*$$ topology, then Hardy-kind $$hk_{(p',q',s)_{\alpha which proves to predual Moreover, prove invariance with respect (1,p)$$ where $$p'$$ $$q'$$ denotes conjugate number p q, respectively. All these results are new even for John–Nirenberg space.