Equivalent Norms of $$cmo^{p}(\mathbb {R}^{n})$$ and Applications

Abstract

In this paper, we prove that $$cmo^{p}(\mathbb {R}^{n})$$ and $$\Lambda _{n(\frac{1}{p}-1)}$$ , the dual spaces of local Hardy space $$h^{p}(\mathbb {R}^{n})$$ , are coincide with equivalent norms for $$\frac{n}{n+1}<p\le 1$$ . Moreover, this space can be characterized by another simple norm. As an application, we prove the $$h^{p}(\mathbb {R}^{n})$$ boundedness of inhomogeneous para-product operators.