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Article

Liu, Suying ; Yang, Minghua
The weighted Hardy spaces associated to self-adjoint operators and their duality on product spaces. (English). Czechoslovak Mathematical Journal, vol. 68 (2018), issue 2, pp. 415-431
MSC: 42B30, 42B35, 47F05 | MR 3819181 | Zbl 06890380 | DOI: 10.21136/CMJ.2018.0469-16
Keywords:
weighted Hardy space; operator; Gaussian estimate; duality; product space
Summary:
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 $H^{p}_{L,w}({\mathbb R}^n\times {\mathbb R}^n)$, $0<p\leq 1$ 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 ${\rm BMO}_{L,w}({\mathbb R}^n\times {\mathbb R}^n)$.
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