Zobrazeno 1 - 10
of 171
pro vyhledávání: '"Lie, Victor"'
Autor:
Hsu, Martin, Lie, Victor
Given a curve $\vec{\gamma}=(t^{\alpha_1}, t^{\alpha_2}, t^{\alpha_3})$ with $\vec{\alpha}=(\alpha_1,\alpha_2,\alpha_3)\in \mathbb{R}_{+}^3$, we define the Carleson-Radon transform along $\vec{\gamma}$ by the formula $$ C_{[\vec{\alpha}]}f(x,y):=\sup
Externí odkaz:
http://arxiv.org/abs/2411.01660
Autor:
Gaitan, Alejandra, Lie, Victor
Building on arXiv:1902.03807, this paper develops a unifying study on the boundedness properties of several representative classes of hybrid operators, i.e. operators that enjoy both zero and non-zero curvature features. Specifically, via the LGC-met
Externí odkaz:
http://arxiv.org/abs/2402.03451
Autor:
Hu, Bingyang, Lie, Victor
Building on the (Rank I) LGC-methodology introduced by the second author and on the novel perspective employed in the time-frequency discretization of the non-resonant bilinear Hilbert--Carleson operator, we develop a new, versatile method -- referre
Externí odkaz:
http://arxiv.org/abs/2308.10706
Publikováno v:
In Advances in Mathematics December 2024 458 Part A
In this paper we introduce the class of bilinear Hilbert--Carleson operators $\{BC^a\}_{a>0}$ defined by $$ BC^{a}(f,g)(x):= \sup_{\lambda\in {\mathbb R}} \Big|\int f(x-t)\, g(x+t)\, e^{i\lambda t^a} \, \frac{dt}{t} \Big| $$ and show that in the non-
Externí odkaz:
http://arxiv.org/abs/2106.09697
Autor:
Gaitan, Alejandra, Lie, Victor
Let $\mathcal{N}\mathcal{F}$ be the class of smooth non-flat curves near the origin and near infinity previously introduced by the second author and let $\gamma\in\mathcal{N}\mathcal{F}$. We show - via a unifying approach relative to the corresponden
Externí odkaz:
http://arxiv.org/abs/1903.11002
Autor:
Lie, Victor
In the present paper and its sequel "A unified approach to three themes in harmonic analysis ($2^{nd}$ part)", we address three rich historical themes in harmonic analysis that rely fundamentally on the concept of non-zero curvature. Namely, we focus
Externí odkaz:
http://arxiv.org/abs/1902.03807
Autor:
Lie, Victor
We prove that the lacunary Carleson operator is bounded from $L \log L$ to $L^{1}$. This result is sharp. The proof is based on two newly introduced concepts: 1) the \emph{time-frequency regularization of a measurable set} and 2) the \emph{set-resolu
Externí odkaz:
http://arxiv.org/abs/1902.03630
Autor:
Lie, Victor
We prove the $L^p$-boundedness, $1
Externí odkaz:
http://arxiv.org/abs/1712.03092
Autor:
Lie, Victor
Publikováno v:
Annals of Mathematics, 2020 Jul 01. 192(1), 47-163.
Externí odkaz:
https://www.jstor.org/stable/10.4007/annals.2020.192.1.2