Marcinkiewicz-Type Spectral Multipliers on Hardy and Lebesgue Spaces on Product Spaces of Homogeneous Type

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• 作者：Peng Chen ; Xuan Thinh Duong ; Ji Li…
• 关键词：Marcinkiewicz ; type spectral multipliers ; Hardy spaces ; Nonnegative self ; adjoint operators ; Restriction type estimates ; Finite propagation speed property
• 刊名：Journal of Fourier Analysis and Applications
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：23
• 期：1
• 页码：21-64
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Fourier Analysis; Signal,Image and Speech Processing; Abstract Harmonic Analysis; Approximations and Expansions; Partial Differential Equations; Mathematical Methods in Physics;
• 出版者：Springer US
• ISSN：1531-5851
• 卷排序：23

文摘

Let \(X_1\) and \(X_2\) be metric spaces equipped with doubling measures and let \(L_1\) and \(L_2\) be nonnegative self-adjoint operators acting on \(L^2(X_1)\) and \(L^2(X_2)\) respectively. We study multivariable spectral multipliers \(F(L_1, L_2)\) acting on the Cartesian product of \(X_1\) and \(X_2\). Under the assumptions of the finite propagation speed property and Plancherel or Stein–Tomas restriction type estimates on the operators \(L_1\) and \(L_2\), we show that if a function F satisfies a Marcinkiewicz-type differential condition then the spectral multiplier operator \(F(L_1, L_2)\) is bounded from appropriate Hardy spaces to Lebesgue spaces on the product space \(X_1\times X_2\). We apply our results to the analysis of second-order elliptic operators in the product setting, specifically Riesz-transform-like operators and double Bochner–Riesz means.