CHEN, Peng; OUHABAZ, El Maati; SIKORA, Adam; YAN, Lixin

doi:10.1007/s11854-016-0021-0

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CHEN, Peng
Department of Mathematics

OUHABAZ, El Maati
Institut de Mathématiques de Bordeaux [IMB]

SIKORA, Adam
Macquarie University

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Journal d'analyse mathématique. 2016, vol. 129, n° 1, p. 219-283

Springer

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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 di erential operators and recover some known results. Our examples include Schr¨odinger operators with inverse square potentials on Rn, the harmonic oscillator, elliptic operators on compact manifolds and Schr¨odinger operators on asymptotically conic manifolds.< Réduire

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RESTRICTION ESTIMATES, SHARP SPECTRAL MULTIPLIERS AND ENDPOINT ESTIMATES FOR BOCHNER-RIESZ MEANS

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