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.

中文翻译：

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$$ cmo ^ {p}（\ mathbb {R} ^ {n}）$$ cmop（R n）的等价范数和应用

在本文中，我们证明\（cmo ^ {p}（\ mathbb {R} ^ {n}）\）和\（\ Lambda _ {n（\ frac {1} {p} -1）} \），局部Hardy空间\（h ^ {p}（\ mathbb {R} ^ {n}）\）的对偶空间与\（\ frac {n} {n + 1} <p \ le 1 \）。而且，该空间可以用另一个简单的范数来表征。作为应用，我们证明了非齐次副乘算子的\（h ^ {p}（\ mathbb {R} ^ {n}）\）有界。