LOCALIZED MORREY-CAMPANATO SPACES ON METRIC MEASURE SPACES AND APPLICATIONS TO SCHRODINGER OPERATORS
LOCALIZED MORREY-CAMPANATO SPACES ON METRIC MEASURE SPACES AND APPLICATIONS TO SCHRODINGER OPERATORS
复制标题
公制测度空间上的定域莫雷-坎帕纳托空间及其在薛定谔算子中的应用
DOI：
10.1215/00277630-2009-008
复制
发表时间：
2010-06-01
影响因子：
0.8
通讯作者：
Zhou, Yuan
中科院分区：
文献类型：
--
作者：
Yang, Dachun;Yang, Dongyong;Zhou, Yuan
Let X be a space of homogeneous type in the sense of Coifman and Weiss, and let 7) be a collection of balls in X. The authors introduce the localized atomic Hardy space H-D(p,q)(X)with p is an element of (0,1] and q is an element of [1, infinity] boolean AND (p, infinity], the localized Morrey-Campanato space epsilon(alpha,p)(D)(X), and the localized MorreyCampanato-BLO (bounded lower oscillation) space (epsilon) over tilde (alpha,p)(D)(X) with alpha is an element of R and p is an element of (0, infinity), and they establish their basic properties, including H-D(p,q)(X) = H-D(p,infinity)(X) and several equivalent characterizations for epsilon(alpha,p)(D)(X) and (epsilon) over tilde (alpha,p)(D)(X). In particular, the authors prove that when alpha > 0 and p is an element of [1, infinity), then (epsilon) over tilde (alpha,p)(D)(X) = epsilon(alpha,p)(D)(X) = Lip(D)(alpha; X), and when p is an element of (0,1], then the dual space of H-D(p,infinity)(X) is epsilon(1/p-1,1)(D)(X). Let rho be an admissible function modeled on the known auxiliary function determined by the Schrodinger operator. Denote the spaces epsilon(alpha,p)(D)(X) and (epsilon) over tilde (alpha,p)(D)(X), respectively, by epsilon(alpha,p)(rho)(X) and (epsilon) over tilde (alpha,p)(rho)(X), when D is determined by p. The authors then obtain the boundedness from epsilon(alpha,p)(rho)(X) to (epsilon) over tilde (alpha,p)(rho)(X) of the radial and the Poisson semigroup maximal functions and the Littlewood-Paley g-function, which are defined via kernels modeled on the semigroup generated by the Schrodinger operator. These results apply in a wide range of settings, for instance, the Schrodinger operator or the degenerate Schrodinger operator on R-d, or the sub-Laplace Schrodinger operator on Heisenberg groups or connected and simply connected nilpotent Lie groups.
