A counterexample for local smoothing for averages over curves
Abstract
We provide a new necessary condition for local smoothing estimates for the averaging operator defined by convolution with a measure supported on a smooth non-degenerate curve in R n \mathbb {R}^n for n ≥ 3 n \geq 3 . This demonstrates a limitation in the strength of local smoothing estimates towards establishing bounds for the corresponding maximal functions when n ≥ 5 n \geq 5 .
Fields of Study & Subjects
Advanced Harmonic Analysis Research
Holomorphic and Operator Theory
Mathematical Analysis and Transform Methods
Publication details
- Journal / source
- Proceedings of the American Mathematical Society
- Publication date
- 16 July 2026
- Language
- EN