Bounds on the maximal Bochner-Riesz means for elliptic operators
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- by Peng Chen, Sanghyuk Lee, Adam Sikora and Lixin Yan PDF
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Abstract:
We investigate $L^p$ boundedness of the maximal Bochner-Riesz means for self-adjoint operators of elliptic-type. Assuming the finite speed of propagation for the associated wave operator, from the restriction-type estimates we establish the sharp $L^p$ boundedness of the maximal Bochner-Riesz means for the elliptic operators. As applications, we obtain the sharp $L^p$ maximal bounds for the Schrödinger operators on asymptotically conic manifolds, elliptic operators on compact manifolds, or the Hermite operator and its perturbations on $\mathbb {R}^n$.References
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Additional Information
- Peng Chen
- Affiliation: Department of Mathematics, Sun Yat-sen University, Guangzhou, 510275, People’s Republic of China
- MR Author ID: 951344
- Email: chenpeng3@mail.sysu.edu.cn
- Sanghyuk Lee
- Affiliation: School of Mathematical Sciences, Seoul National University, Seoul 151-742, Repulic of Korea
- MR Author ID: 681594
- Email: shklee@snu.ac.kr
- Adam Sikora
- Affiliation: Department of Mathematics, Macquarie University, NSW 2109, Australia
- MR Author ID: 292432
- Email: adam.sikora@mq.edu.au
- Lixin Yan
- Affiliation: Department of Mathematics, Sun Yat-sen University, Guangzhou, 510275, People’s Republic of China; and Department of Mathematics, Macquarie University, NSW 2109, Australia
- MR Author ID: 618148
- Email: mcsylx@mail.sysu.edu.cn
- Received by editor(s): May 24, 2018
- Received by editor(s) in revised form: October 23, 2018
- Published electronically: March 2, 2020
- Additional Notes: Peng Chen is the corresponding author
The first author was supported by Guangdong Natural Science Foundation 2016A030313351
The second author was partially supported by NRF (Republic of Korea) grant No. NRF-2018R1A2B2006298
The third author was partly supported by Australian Research Council Discovery Grant DP DP160100941.
The fourth author was supported by the NNSF of China, Grant No. 11521101 and 11871480, and by Australian Research Council Discovery Grant DP170101060. - © Copyright 2020 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 373 (2020), 3793-3828
- MSC (2010): Primary 42B15, 42B25, 47F05
- DOI: https://doi.org/10.1090/tran/8024
- MathSciNet review: 4105510