Tohoku Mathematical Journal
2021
September
SECOND SERIES VOL. 73, NO. 3

Tohoku Math. J.
73 (2021), 403-419

Title THE COMMUTATORS OF BOCHNER-RIESZ OPERATORS FOR ELLIPTIC OPERATORS

Author Peng Chen, Xiaoxiao Tian and Lesley A. Ward

(Received October 2, 2019)
Abstract. We study $L^p$-boundedness of commutators of Bochner-Riesz operators for elliptic self-adjoint operators which satisfy the finite speed of propagation property for the corresponding wave equation. Our results can be applied to Schrödinger operators with inverse square potentials on $\mathbb{R}^n$, elliptic operators on compact manifolds, and Schrödinger operators on asymptotically conic manifolds.
 Our proof is new even for the commutator of the classical Bochner-Riesz operator when $L$ is the Laplace operator $\Delta=\sum_{i=1}^n\partial_{x_i}^2$ on the Euclidean space $\mathbb{R}^n$.

Mathematics Subject Classification. Primary 42B15; Secondary 42B20, 47F05.
Key words and phrases. Commutators, Bochner-Riesz operators, spectral multipliers.

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