Restriction estimates, sharp spectral multipliers and endpoint estimates for Bochner-Riesz means
By Peng Chen, El-Maati Ouhabaz, Adam S. Sikora, Lixin Yan. 2012
84 citations recorded by the source corpus.
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.
Subfields: Applied Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/ab56348da2e65747c207728a35b63466dfb175e9
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In Applied Mathematics
- Rowan Killip
- Changxing Miao
- Jiqiang Zheng
- Matthias W. Uhl
- Monica Visan
- P. Kunstmann
- Barry Simon
- B. Dodson
In Mathematical Physics
- Rowan Killip
- Changxing Miao
- Monica Visan
- Jiqiang Zheng
- Matthias W. Uhl
- P. Kunstmann
- B. Dodson
- Aynur Bulut
Citations in the corpus
- Spectral multiplier theorems of H\"ormander type on Hardy and Lebesgue spaces (2012, methodology): “Examples of operators to which our results apply but those in [28, 15, 29, 30] are not applicable include higher order elliptic operators in divergence form with bounded complex-valued coefficients on RD (cf.”
- Sobolev spaces adapted to the Schrödinger operator with inverse-square potential (2015, background): “s, the stated range of pis sharp, including the question of endpoints. Several authors have developed general multiplier theorems under weaker hypotheses on the heat kernel. In particular, the papers [6, 10] explicitly verify that the multiplier theorems proved therein apply to the operators La for ”