Czechoslovak Mathematical Journal, Vol. 68, No. 2, pp. 415-431, 2018
The weighted Hardy spaces associated to self-adjoint operators and their duality on product spaces
Suying Liu, Minghua Yang
Received September 7, 2016. First published February 7, 2018.
Abstract: Let $L$ be a non-negative self-adjoint operator acting on $L^2(\mathbb R^n)$ satisfying a pointwise Gaussian estimate for its heat kernel. Let $w$ be an $A_r$ weight on $\mathbb R^n\times{\mathbb R}^n$, $1<r<\infty$. In this article we obtain a weighted atomic decomposition for the weighted Hardy space $H^p_{L,w}(\mathbb R^n\times\mathbb R^n)$, $0<p\leq1$ associated to $L$. Based on the atomic decomposition, we show the dual relationship between $H^1_{L,w}(\mathbb R^n\times\mathbb R^n)$ and ${\rm BMO}_{L,w}(\mathbb R^n\times\mathbb R^n)$.
Keywords: weighted Hardy space; operator; Gaussian estimate; duality; product space
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Affiliations: Suying Liu, School of Science, Northwestern Polytechnical University, 127 Youyi W Rd, Xian, 710000, Shaanxi, P. R. China, e-mail: liusuying0319@126.com; Minghua Yang, School of Information Technology, Jiangxi University of Finance and Economics, Jupu Rd, Nanchang, 330032, Jiangxi, P. R. China, e-mail: ymh20062007@163.com
