Taiwanese Journal of Mathematics


Suying Liu, Kai Zhao, and Shujuan Zhou

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Let $L$ be a non-negative self-adjoint operator satisfying a pointwise Guassian estimate for its heat kernel. Let $w$ be some $A_s$ weight on $\mathbb{R}^n$. In this paper, we obtain a weighted $(p,q)-$atomic decomposition with $q\geq s$ for the weighted Hardy spaces $H^p_{L,w}(\mathbb{R}^n)$, $0\lt p\leq 1$. We also introduce the suitable weighted BMO spaces $BMO^p_{L,w}$. Then the duality between $H^1_{L,w}(\mathbb{R}^n)$ and $BMO_{L,w}$ is established.

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Taiwanese J. Math., Volume 18, Number 5 (2014), 1663-1678.

First available in Project Euclid: 10 July 2017

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Zentralblatt MATH identifier

Primary: 42B20: Singular and oscillatory integrals (Calderón-Zygmund, etc.) 42B30: $H^p$-spaces
Secondary: 47F05: Partial differential operators [See also 35Pxx, 58Jxx] (should also be assigned at least one other classification number in section 47)

weighted Hardy space self-adjoint operator weighted atom $BMO_{L,w}$


Liu, Suying; Zhao, Kai; Zhou, Shujuan. WEIGHTED HARDY SPACES ASSOCIATED TO SELF-ADJOINT OPERATORS AND $BMO_{L,w}$. Taiwanese J. Math. 18 (2014), no. 5, 1663--1678. doi:10.11650/tjm.18.2014.3759. https://projecteuclid.org/euclid.twjm/1499706532

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