Acta mathematica scientia,Series B ›› 2014, Vol. 34 ›› Issue (3): 891-904.doi: 10.1016/S0252-9602(14)60057-6

• Articles • Previous Articles     Next Articles

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

 YAN Xue-Fang   

  1. Department of Mathematics, Sun Yat-sen (Zhongshan) University, Guangzhou 510275, China;College of Mathematics and Information Science, Heibei Normal University, Shijiazhuang 050016, China
  • Received:2013-06-28 Revised:2013-09-29 Online:2014-05-20 Published:2014-05-20

Abstract:

Let (X, d, μ) be a metric measure space endowed with a metric d and a nonneg-ative Borel doubling measure μ. Let L be a second order non-negative self-adjoint operator on L2(X). Assume that the semigroup etL 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 GδL) arising from Bochner-Riesz means associated to L is bounded from the Hardy spaces HpL(X) to Lp(X) for all 0 < p ≤1.

Key words: Stein´s square function, non-negative self-adjoint operator, Hardy spaces, Davies-Gaffney estimate, Plancherel type estimate

CLC Number: 

  • 42B15
Trendmd