Boundedness of Stein’s square functions and Bochner-Riesz means associated to operators on hardy spaces

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• 作者：Xuefang Yan
• 关键词：non ; negative self ; adjoint operator ; Stein’s square function ; Bochner ; Riesz means ; Davies ; Gaffney estimate ; molecule Hardy space ; 42B15 ; 42B25 ; 47F05
• 刊名：Czechoslovak Mathematical Journal
• 出版年：2015
• 出版时间：March 2015
• 年：2015
• 卷：65
• 期：1
• 页码：61-82
• 全文大小：248 KB
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• 作者单位：Xuefang Yan (1)
  
  1. College of Mathematics and Information Science, Heibei Normal University, No. 20 South 2nd Ring Road (East), Shijiazhuang, Hebei Prov., 050024, P.R. China
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  Analysis
  Convex and Discrete Geometry
  Ordinary Differential Equations
  Mathematical Modeling and IndustrialMathematics
  
• 出版者：Springer Netherlands
• ISSN：1572-9141

文摘

Let (X, d, μ) be a metric measure space endowed with a distance d and a nonnegative Borel doubling measure μ. Let L be a non-negative self-adjoint operator of order m on L 2(X). Assume that the semigroup e?em class="EmphasisTypeItalic">tL generated by L satisfies the Davies-Gaffney estimate of order m and L satisfies the Plancherel type estimate. Let H _L p (X) be the Hardy space associated with L. We show the boundedness of Stein’s square function \({g_\delta }(L)\) arising from Bochner-Riesz means associated to L from Hardy spaces H _L p (X) to L p (X), and also study the boundedness of Bochner-Riesz means on Hardy spaces H _L p (X) for 0 < p ?1.