Estimates for strongly singular operators along curves
Abstract
Abstract For an appropriate function f on the plane, we study the operator $$\begin{align*}Tf(x,y) = \lim_{\varepsilon\to 0} \int_\varepsilon^1 f(x-t,y-\phi(t)) \frac{e^{2\pi i \gamma(t)}}{\psi(t)} dt, \end{align*}$$ T f ( x , y ) = lim ε → 0 ∫ ε 1 f ( x − t , y − ϕ ( t ) ) e 2 π i γ ( t ) ψ ( t ) d t , where phi $\phi $ ϕ is convex and psi $\psi $ ψ and gamma $\gamma $ γ are functions defined near the origin such that psi left parenthesis t right parenthesis right arrow 0 $\psi (t)\to 0$ ψ ( t ) → 0 and
Fields of Study & Subjects
Holomorphic and Operator Theory
Spectral Theory in Mathematical Physics
Advanced Banach Space Theory
Publication details
- Journal / source
- Canadian Mathematical Bulletin
- Publisher
- Canadian Mathematical Society
- Pages
- 1–16
- Publication date
- 30 April 2026
- Language
- EN