naa a22 4500 510760732 CHVBK 20180411083138.0 cr unu---uuuuu 180411e20130101xx s 000 0 eng 10.1007/s13163-011-0092-5 doi (NATIONALLICENCE)springer-10.1007/s13163-011-0092-5 Endpoint boundedness of Riesz transforms on Hardy spaces associated with operators [Elektronische Daten] [Jun Cao, Dachun Yang, Sibei Yang] Let L 1 be a nonnegative self-adjoint operator in L 2(ℝ 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 Schrödinger operator −Δ+V, where Δ is the Laplace operator on ℝ 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∈{1, 2}. 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 (ℝ 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 (ℝ n ) when p∈(n/(n+1), 1]. Revista Matemática Complutense, 2011 Riesz transform nationallicence Davies-Gaffney estimate nationallicence Schrödinger operator nationallicence Second order elliptic operator nationallicence Hardy space nationallicence Weak Hardy space nationallicence Cao Jun School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, 100875, Beijing, People's Republic of China aut Yang Dachun School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, 100875, Beijing, People's Republic of China aut Yang Sibei School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, 100875, Beijing, People's Republic of China aut Revista Matemática Complutense Springer Milan 26/1(2013-01-01), 99-114 1139-1138 26:1<99 2013 26 13163 https://doi.org/10.1007/s13163-011-0092-5 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s13163-011-0092-5 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Cao Jun School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, 100875, Beijing, People's Republic of China aut NATIONALLICENCE 700 1- Yang Dachun School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, 100875, Beijing, People's Republic of China aut NATIONALLICENCE 700 1- Yang Sibei School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, 100875, Beijing, People's Republic of China aut NATIONALLICENCE 773 0- Revista Matemática Complutense Springer Milan 26/1(2013-01-01), 99-114 1139-1138 26:1<99 2013 26 13163 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer