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

doi:10.1016/S0252-9602(14)60057-6

数学物理学报(英文版) ›› 2014, Vol. 34 ›› Issue (3): 891-904.doi: 10.1016/S0252-9602(14)60057-6

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

闫雪芳

Department of Mathematics, Sun Yat-sen (Zhongshan) University, Guangzhou 510275, China；College of Mathematics and Information Science, Heibei Normal University, Shijiazhuang 050016, China

收稿日期:2013-06-28 修回日期:2013-09-29 出版日期:2014-05-20 发布日期:2014-05-20

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

YAN Xue-Fang

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

摘要/Abstract

摘要：

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 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 G_δL) arising from Bochner-Riesz means associated to L is bounded from the Hardy spaces H^p_L(X) to L^p(X) for all 0 < p ≤1.

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

Abstract:

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

中图分类号:

42B15

闫雪芳. BOUNDEDNESS OF STEIN´S SQUARE FUNCTIONS ASSOCIATED TO OPERATORS ON HARDY SPACES[J]. 数学物理学报(英文版), 2014, 34(3): 891-904.

YAN Xue-Fang. BOUNDEDNESS OF STEIN´S SQUARE FUNCTIONS ASSOCIATED TO OPERATORS ON HARDY SPACES[J]. Acta mathematica scientia,Series B, 2014, 34(3): 891-904.

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

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

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