A wavelet characterization for the dual of weighted anisotropic Hardy spaces
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Let $A$ be a general expansive matrix on $\mathbb{R}^n$ and $H_{A,w}^p(\mathbb R^n)$ the weighed anisotropic Hardy space associated to $A$, where $p\in(0,1]$ and $w$ is an anisotropic Muckenhoupt weight. In this article, the authors first introduce the weighted anisotropic Carleson measure space ${\mathrm{CMO}}_{A,w}^{p}(\mathbb{R}^n)$ in terms of wavelets. Then, using the known wavelet characterization of $H_{A,w}^p(\mathbb R^n)$ and establishing a duality relation between two sequence spaces, the authors prove that the space ${\mathrm{CMO}}_{A,w}^{p}(\mathbb{R}^n)$ is the dual space of $H_{A,w}^p(\mathbb R^n)$. As an application, the authors give a wavelet characterization of weighed anisotropic Campanato spaces. All these results are new even for the parabolic Hardy space or the anisotropic Hardy space $H_A^p(\mathbb R^n)$.
Abstract
Let $A$ be a general expansive matrix on $\mathbb{R}^n$ and $H_{A,w}^p(\mathbb R^n)$ the weighed anisotropic Hardy space associated to $A$, where $p\in(0,1]$ and $w$ is an anisotropic Muckenhoupt weight. In this article, the authors first introduce the weighted anisotropic Carleson measure space ${\mathrm{CMO}}_{A,w}^{p}(\mathbb{R}^n)$ in terms of wavelets. Then, using the known wavelet characterization of $H_{A,w}^p(\mathbb R^n)$ and establishing a duality relation between two sequence spaces, the authors prove that the space ${\mathrm{CMO}}_{A,w}^{p}(\mathbb{R}^n)$ is the dual space of $H_{A,w}^p(\mathbb R^n)$. As an application, the authors give a wavelet characterization of weighed anisotropic Campanato spaces. All these results are new even for the parabolic Hardy space or the anisotropic Hardy space $H_A^p(\mathbb R^n)$.