Endpoint boundedness of Riesz transforms on Hardy spaces associated with operators
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- 作者：Jun Cao (1)
Dachun Yang (1)
Sibei Yang (1) - 关键词：Riesz transform ; Davies ; Gaffney estimate ; Schr枚dinger operator ; Second order elliptic operator ; Hardy space ; Weak Hardy space ; 47B06 ; 42B20 ; 42B25 ; 42B30 ; 35J10
- 刊名：Revista Matem篓垄tica Complutense
- 出版年：2013
- 出版时间：January 2013
- 年：2013
- 卷：26
- 期：1
- 页码：99-114
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Dachun Yang (1)
Sibei Yang (1)
1. School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing, 100875, People鈥檚 Republic of China - ISSN：1988-2807
文摘
Let L 1 be a nonnegative self-adjoint operator in L 2(鈩?sup class="a-plus-plus"> n ) satisfying the Davies-Gaffney estimates and L 2 a second order divergence form elliptic operator with complex bounded measurable coefficients. A typical example of L 1 is the Schr枚dinger operator 鈭捨?V, where 螖 is the Laplace operator on 鈩?sup class="a-plus-plus"> n and $0\le V\in L^{1}_{\mathop{\mathrm{loc}}} ({\mathbb{R}}^{n})$ . Let $H^{p}_{L_{i}}(\mathbb{R}^{n})$ be the Hardy space associated to L i for i鈭坽1,鈥?}. In this paper, the authors prove that the Riesz transform $D (L_{i}^{-1/2})$ is bounded from $H^{p}_{L_{i}}(\mathbb{R}^{n})$ to the classical weak Hardy space WH p (鈩?sup class="a-plus-plus"> n ) in the critical case that p=n/(n+1). Recall that it is known that $D(L_{i}^{-1/2})$ is bounded from $H^{p}_{L_{i}}(\mathbb{R}^{n})$ to the classical Hardy space H p (鈩?sup class="a-plus-plus"> n ) when p鈭?n/(n+1),鈥?].