Duality of Hardy and BMO spaces associated with operators with heat kernel bounds期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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Duality of Hardy and BMO spaces associated with operators with heat kernel bounds

Authors:	Xuan Thinh Duong Lixin Yan

Institution:	Department of Mathematics, Macquarie University, NSW 2109, Australia ; Department of Mathematics, Macquarie University, NSW 2109, Australia and Department of Mathematics, Zhongshan University, Guangzhou, 510275, People's Republic of China

Abstract:	Let be the infinitesimal generator of an analytic semigroup on $L^2({\mathbb R}^n)$ with suitable upper bounds on its heat kernels. Auscher, Duong, and McIntosh defined a Hardy space by means of an area integral function associated with the operator . By using a variant of the maximal function associated with the semigroup $\{e^{-tL}\}_{t\geq 0}$ , a space ${\rm BMO}_L$ of functions of BMO type was defined by Duong and Yan and it generalizes the classical BMO space. In this paper, we show that if has a bounded holomorphic functional calculus on $L^2({\mathbb R}^n)$ , then the dual space of is ${\rm BMO}_{L^{\ast}}$ where $L^{\ast}$ is the adjoint operator of . We then obtain a characterization of the space ${\rm BMO}_L$ in terms of the Carleson measure. We also discuss the dimensions of the kernel spaces ${\mathcal K}_L$ of BMO $_{ L}$ when is a second-order elliptic operator of divergence form and when is a Schrödinger operator, and study the inclusion between the classical BMO space and ${\rm BMO}_L$ spaces associated with operators.

Keywords:	Hardy space BMO semigroup holomorphic functional calculi tent space Carleson measure second-order elliptic operator Schr\"odinger operator

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