On a planar Pierce–Yung operator
Abstract
We show that the operator \begin{equation*} \mathcal{C} f(x,y) := \sup_{v\in \mathbb{R}} \Big|\mathrm{p.v.} \int_{\mathbb{R}} f(x-t, y-t^2) e^{i v t^3} \frac{\mathrm{d} t}{t} \Big| \end{equation*} is bounded on $L^p(\mathbb{R}^2)$ for every $1 < p < \infty$. This gives an affirmative answer to a question of Pierce and Yung.
Fields of Study & Subjects
Spectral Theory in Mathematical Physics
Matrix Theory and Algorithms
Holomorphic and Operator Theory
Publication details
- Journal / source
- Duke Mathematical Journal
- Publisher
- Duke University Press
- Volume
- 175
- Issue
- 5
- Pages
- 903-958
- Publication date
- 1 April 2026
- Language
- EN