A Littlewood–Paley Type Decomposition and Weighted Hardy Spaces Associated with Operators

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• 作者：Xuan Thinh Duong ; Ji Li ; Lixin Yan
• 关键词：Hardy spaces ; Weights ; Non ; negative self ; adjoint operators ; Heat semigroup ; Area and Littlewood–Paley functions ; Moser type boundedness condition ; Space of homogeneous type
• 刊名：Journal of Geometric Analysis
• 出版年：2016
• 出版时间：April 2016
• 年：2016
• 卷：26
• 期：2
• 页码：1617-1646
• 全文大小：587 KB
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• 作者单位：Xuan Thinh Duong (1)
  Ji Li (1)
  Lixin Yan (2)
  
  1. Department of Mathematics, Macquarie University, Sydney, NSW, 2109, Australia
  2. Department of Mathematics, Sun Yat-sen (Zhongshan) University, Guangzhou, 510275, People’s Republic of China
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Differential Geometry
  Convex and Discrete Geometry
  Fourier Analysis
  Abstract Harmonic Analysis
  Dynamical Systems and Ergodic Theory
  Global Analysis and Analysis on Manifolds
  
• 出版者：Springer New York
• ISSN：1559-002X

文摘

Let \((X, d, \mu )\) be a metric measure space endowed with a distance \(d\) and a nonnegative Borel doubling measure \(\mu \). 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 Gaussian upper bounds. In this article we establish a discrete characterization of weighted Hardy spaces \(H_{L, S, w}^{p}(X)\) associated with \(L\) in terms of the area function characterization, and prove its weighted atomic decomposition, where \(0<p\le 1\) and a weight \(w\) is in the Muckenhoupt class \(A_{\infty }\). Further, we introduce a Moser type estimate for \(L\) to show the discrete characterization for the weighted Hardy spaces \(H_{L, G, w}^{p}(X)\) associated with \(L\) in terms of the Littlewood–Paley function and obtain the equivalence between the weighted Hardy spaces in terms of the Littlewood–Paley function and area function.