BOUNDEDNESS OF STEIN'S SQUARE FUNCTIONS ASSOCIATED TO OPERATORS ON HARDY SPACES

作     者：闫雪芳 Xuefang YAN

作者机构：Department of MathematicsSun Yat-sen (Zhongshan) University College of Mathematics and Information ScienceHeibei Normal University 

出 版 物：《Acta Mathematica Scientia》 (数学物理学报（B辑英文版）)

年 卷 期：2014年第34卷第3期

页      面：891-904页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

主　　题：Stein's square function non-negative self-adjoint operator Hardy spaces Davies- Gaffney estimate Plancherel type estimate 

摘      要：Let （X, d,μ） be a metric measure space endowed with a metric d and a nonnegative Borel doubling measure μ. Let L be a second order non-negative self-adjoint operator on L^2（X）. Assume that the semigroup e^-tL generated by L satisfies the Davies-Gaffney estimates. Also, assume that L satisfies Plancherel type estimate. Under these conditions, we show that Stein＇s square function Gδ（L） arising from Bochner-Riesz means associated to L is bounded from the Hardy spaces HL^p（X） to L^p（X） for all 0 〈 p ≤ 1.