Localized Morrey-Campanato spaces on metric measure spaces and applications to Schrüdinger operators

By Dachun Yang, Dongyong Yang, Yuan Zhou. Nagoya mathematical journal, 2009

85 citations recorded by the source corpus.

Abstract Let be a space of homogeneous type in the sense of Coifman and Weiss, and let be a collection of balls in . The authors introduce the localized atomic Hardy space the localized Morrey-Campanato space and the localized Morrey-Campanato-BLO (bounded lower oscillation) space with α ∊ ℝ and p ∊ (0, ∞) , and they establish their basic properties, including and several equivalent characterizations for In particular, the authors prove that when α > 0 and p ∊ [1, ∞), then and when p ∈(0,1], then the dual space of is Let ρ be an admissible function modeled on the known auxiliary function determined by the Schrödinger operator. Denote the spaces and , respectively, by and when is determined by ρ. The authors then obtain the boundedness from 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 Schrödinger operator. These results apply in a wide range of settings, for instance, the Schrödinger operator or the degenerate Schrödinger operator on ℝ d , or the sub-Laplace Schrödinger operator on Heisenberg groups or connected and simply connected nilpotent Lie groups.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/5913e89b6813861615139076d3e64a03209d0e1f