Zobrazeno 1 - 10
of 171
pro vyhledávání: '"Guo, Shaoming"'
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 <
Externí odkaz:
http://arxiv.org/abs/2407.07563
Autor:
Chen, Mingfeng, Gan, Shengwen, Guo, Shaoming, Hickman, Jonathan, Iliopoulou, Marina, Wright, James
We consider a class of H\"ormander-type oscillatory integral operators in $\mathbb{R}^n$ for $n \geq 3$ odd with real analytic phase. We derive weak conditions on the phase which ensure $L^p$ bounds beyond the universal $p \geq 2 \cdot \frac{n+1}{n-1
Externí odkaz:
http://arxiv.org/abs/2407.06980
Autor:
Chen, Mingfeng, Guo, Shaoming
We show that Nikodym sets and local smoothing estimates for linear wave equations form a dichotomy: If Nikodym sets for a family of curves exist, then the related maximal operator is not bounded on $L^p(\mathbb{R}^2)$ for any $p<\infty$; if Nikodym s
Externí odkaz:
http://arxiv.org/abs/2402.15476
We prove that if $f\in L^p(\mathbb{R}^k)$ with $p<(k^2+k+2)/2$ satisfies that $\widehat{f}$ is supported on a small perturbation of the moment curve in $\mathbb{R}^k$, then $f$ is identically zero. This improves the more general result of Agranovsky
Externí odkaz:
http://arxiv.org/abs/2311.11529
We consider Carleson-Sj\"{o}lin operators on Riemannian manifolds that arise naturally from the study of Bochner-Riesz problems on manifolds. They are special cases of H\"{o}rmander-type oscillatory integral operators. We obtain improved $L^p$ bounds
Externí odkaz:
http://arxiv.org/abs/2310.20122
We state a multi-parameter cinematic curvature condition, and prove $L^p$ bounds for related maximal operators. In particular, we verify a local smoothing conjecture of Zahl.
Externí odkaz:
http://arxiv.org/abs/2306.01606
Let $\gamma: [-1, 1]\to \mathbb{R}^n$ be a smooth curve that is non-degenerate. Take $m\le n$ and a Borel set $E\subset [0, 1]^n$. We prove that the orthogonal projection of $E$ to the $m$-th order tangent space of $\gamma$ at $\theta\in [-1, 1]$ has
Externí odkaz:
http://arxiv.org/abs/2211.09508
In this paper, we first generalize the work of Bourgain and state a curvature condition for H\"ormander-type oscillatory integral operators, which we call Bourgain's condition. This condition is notably satisfied by the phase functions for the Fourie
Externí odkaz:
http://arxiv.org/abs/2210.05851
Autor:
Gan, Shengwen, Guo, Shaoming, Guth, Larry, Harris, Terence L. J., Maldague, Dominique, Wang, Hong
Let $\gamma:[0,1]\rightarrow \mathbb{S}^{2}$ be a non-degenerate curve in $\mathbb{R}^3$, that is to say, $\det\big(\gamma(\theta),\gamma'(\theta),\gamma"(\theta)\big)\neq 0$. For each $\theta\in[0,1]$, let $V_\theta=\gamma(\theta)^\perp$ and let $\p
Externí odkaz:
http://arxiv.org/abs/2207.13844