Sharp estimates for oscillatory integral operators via polynomial partitioning
- Submitting institution
-
The University of Kent
- Unit of assessment
- 10 - Mathematical Sciences
- Output identifier
- 17777
- Type
- D - Journal article
- DOI
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10.4310/ACTA.2019.v223.n2.a2
- Title of journal
- Acta Mathematica
- Article number
- -
- First page
- 251
- Volume
- 223
- Issue
- 2
- ISSN
- 0001-5962
- Open access status
- Access exception
- Month of publication
- December
- Year of publication
- 2019
- URL
-
https://kar.kent.ac.uk/75575/
- Supplementary information
-
-
- Request cross-referral to
- -
- Output has been delayed by COVID-19
- No
- COVID-19 affected output statement
- -
- Forensic science
- No
- Criminology
- No
- Interdisciplinary
- No
- Number of additional authors
-
2
- Research group(s)
-
-
- Proposed double-weighted
- Yes
- Double-weighted statement
- In this paper we fully settle a famous question by Hörmander on oscillatory integral operators, standing since 1973. Hörmander's problem lies in controlling wave interference. Aiming to generalise the fundamental, open Fourier restriction conjecture of harmonic analysis, it has connections with PDE, mathematical physics, geometric measure theory and number theory.
We fully determine the behaviour of Hörmander's operators, exploiting an algebraic nature underlying their often pathological mass-compression behaviour. As an application, we derive the best-known bounds on the Bochner-Riesz conjecture of Fourier multiplier theory, a problem under intense focus since revolutionary work of Fefferman (1971), equivalent to the restriction conjecture.
- Reserve for an output with double weighting
- No
- Additional information
- -
- Author contribution statement
- -
- Non-English
- No
- English abstract
- -
