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

Content Provider	Springer Nature Link
Author	Yan, Lixin Duong, Xuan Thinh Chen, Peng Li, Ji Ward, Lesley A.
Copyright Year	2016
Abstract	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.
Ending Page	64
Page Count	44
Starting Page	21
File Format	PDF
ISSN	10695869
e-ISSN	15315851
Journal	Journal of Fourier Analysis and Applications
Issue Number	1
Volume Number	23
Language	English
Publisher	Springer US
Publisher Date	2016-02-25
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Hermitian and normal operators (spectral measures, functional calculus, etc.) Multipliers Nonnegative self-adjoint operators Hardy spaces General topics in linear spectral theory Abstract Harmonic Analysis Mathematical Methods in Physics Fourier Analysis Signal,Image and Speech Processing Marcinkiewicz-type spectral multipliers Approximations and Expansions $H^p$ -spaces Finite propagation speed property Partial Differential Equations Restriction type estimates
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Analysis

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