LOCALIZED HARDY SPACES H1 RELATED TO ADMISSIBLE FUNCTIONS ON RD-SPACES AND APPLICATIONS TO SCHRODINGER OPERATORS
LOCALIZED HARDY SPACES H1 RELATED TO ADMISSIBLE FUNCTIONS ON RD-SPACES AND APPLICATIONS TO SCHRODINGER OPERATORS
复制标题
DOI：
10.1090/s0002-9947-2010-05201-8
复制
发表时间：
2011-03-01
影响因子：
1.3
通讯作者：
Zhou, Yuan
中科院分区：
文献类型：
--
作者：
Yang, Dachun;Zhou, Yuan
Let X be an RD-space, which means that X is a space of homogenous type in the sense of Coifman and Weiss with the additional property that a reverse doubling property holds in X. In this paper, the authors first introduce the notion of admissible functions p and then develop a theory of localized Hardy spaces H-rho(1),(X) associated with p, which includes several maximal function characterizations of H);(X), the relations between Hi(X) and the classical Hardy space H-1 (X) via constructing a kernel function related to p, the atomic decomposition characterization of H-rho(1)(X), and the boundedness of certain localized singular integrals on H-rho(1)(X) via a finite atomic decomposition characterization of some dense subspace of H-rho(1)(X). This theory has a wide range of applications. Even when this theory is applied, respectively, to the Schrodinger operator or the degenerate Schrodinger operator on R-n, or to the sub-Laplace SchrOdinger operator on Heisenberg groups or connected and simply connected nilpotent Lie groups, some new results are also obtained. The Schrodinger operators considered here are associated with nonnegative potentials satisfying the reverse Holder inequality.
