Restriction estimates, sharp spectral multipliers and endpoint estimates for Bochner-Riesz means

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• 作者：Peng Chen ; El Maati Ouhabaz ; Adam Sikora ; Lixin Yan
• 刊名：Journal d'Analyse Math¨¦matique
• 出版年：2016
• 出版时间：July 2016
• 年：2016
• 卷：129
• 期：1
• 页码：219-283
• 全文大小：558 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Analysis
  Functional Analysis
  Dynamical Systems and Ergodic Theory
  Abstract Harmonic Analysis
  Partial Differential Equations
  
• 出版者：Hebrew University Magnes Press
• ISSN：1565-8538
• 卷排序：129

文摘

We consider abstract non-negative self-adjoint operators on L2(X) which satisfy the finite-speed propagation property for the corresponding wave equation. For such operators, we introduce a restriction type condition, which in the case of the standard Laplace operator is equivalent to (p, 2) restriction estimate of Stein and Tomas. Next, we show that in the considered abstract setting, our restriction type condition implies sharp spectral multipliers and endpoint estimates for the Bochner-Riesz summability. We also observe that this restriction estimate holds for operators satisfying dispersive or Strichartz estimates. We obtain new spectral multiplier results for several second order differential operators and recover some known results. Our examples include Schrödinger operators with inverse square potentials on Rn, the harmonic oscillator, elliptic operators on compact manifolds, and Schr¨odinger operators on asymptotically conic manifolds.