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The weighted Hardy spaces associated to self-adjoint operators and their duality on product spaces
Czechoslovak Mathematical Journal, Tome 68 (2018) no. 2, pp. 415-431 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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 ${\mathbb R}^n\times {\mathbb R}^n$, $1$. In this article we obtain a weighted atomic decomposition for the weighted Hardy space $H^{p}_{L,w}({\mathbb R}^n\times {\mathbb R}^n)$, $0$ 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 ${\rm BMO}_{L,w}({\mathbb R}^n\times {\mathbb R}^n)$.
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 ${\mathbb R}^n\times {\mathbb R}^n$, $1$. In this article we obtain a weighted atomic decomposition for the weighted Hardy space $H^{p}_{L,w}({\mathbb R}^n\times {\mathbb R}^n)$, $0$ 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 ${\rm BMO}_{L,w}({\mathbb R}^n\times {\mathbb R}^n)$.
DOI : 10.21136/CMJ.2018.0469-16
Classification : 42B30, 42B35, 47F05
Keywords: weighted Hardy space; operator; Gaussian estimate; duality; product space 
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     author = {Liu, Suying and Yang, Minghua},
     title = {The weighted {Hardy} spaces associated to self-adjoint operators and their duality on product spaces},
     journal = {Czechoslovak Mathematical Journal},
     pages = {415--431},
     year = {2018},
     volume = {68},
     number = {2},
     doi = {10.21136/CMJ.2018.0469-16},
     mrnumber = {3819181},
     zbl = {06890380},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2018.0469-16/}
}
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Liu, Suying; Yang, Minghua. The weighted Hardy spaces associated to self-adjoint operators and their duality on product spaces. Czechoslovak Mathematical Journal, Tome 68 (2018) no. 2, pp. 415-431. doi: 10.21136/CMJ.2018.0469-16

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