The weighted Hardy spaces associated to self-adjoint operators and their duality on product spaces

Liu, Suying ; Yang, Minghua

Czechoslovak Mathematical Journal, Tome 68 (2018) no. 2, pp. 415-431.

Résumé

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 ${\rm BMO}_{L,w}({\mathbb R}^n\times {\mathbb R}^n)$.

Détail

DOI : 10.21136/CMJ.2018.0469-16

Classification : 42B30, 42B35, 47F05
Keywords: weighted Hardy space; operator; Gaussian estimate; duality; product space