Haixia Yu

activity

20182025

most citedBilinear Hilbert Transforms and (Sub)Bilinear Maximal Functions along Convex Curves

2 citations · 5 across the 9 of their papers we have counts for

collaborators

9 papers

math.AP2025

Mixed norm estimates for dilated averages over planar curves

Junfeng Li, Zengjian Lou, Haixia Yu

In this paper, we investigate the mixed norm estimates for the operator $T$ associated with a dilated plane curve $(u t, u γ (t))$ , defined by \[ Tf(x, u) := \int_{0}^{1} f(x_1 - ut,…

math.CA2024★ 1 cited

The Boundedness of the Bilinear Fractional Integrals along Curves

Junfeng Li, Haixia Yu, Minqun Zhao

In this paper, for general curves $(t, γ (t))$ satisfying some suitable curvature conditions, we obtain some $L^{p} (R) \times L^{q} (R) \to L^{r} (R)$ estim…

math.CA2024

$L_{x}^{p} \to L_{x, u}^{q}$ estimates for dilated averages over planar curves

Junfeng Li, Naijia Liu, Zengjian Lou +1

In this paper, we consider the $L_{x}^{p} (R^{2}) \to L_{x, u}^{q} (R^{2} \times [1, 2])$ estimate for the operator $T$ along a dilated plane curve $(u t, u γ (t))$ , where $$…

math.CA2021

Hilbert transforms along variable planar curves: Lipschitz regularity

Naijia Liu, Haixia Yu

In this paper, for $1 < p < \infty$ , we obtain the $L^{p}$ -boundedness of the Hilbert transform $H^{γ}$ along a variable plane curve $(t, u (x_{1}, x_{2}) γ (t))$ , where $u$ is a Lipschitz functio…

math.CA2020★ 1 cited

$L^{p} (R^{2})$ -boundedness of Hilbert Transforms and Maximal Functions along Plane Curves with Two-variable Coefficients

Naijia Liu, Liang Song, Haixia Yu

In this paper, for general plane curves $γ$ satisfying some suitable smoothness and curvature conditions, we obtain the single annulus $L^{p} (R^{2})$ -boundedness of the Hilber…

math.CA2020★ 2 cited

Bilinear Hilbert Transforms and (Sub)Bilinear Maximal Functions along Convex Curves

Junfeng Li, Haixia Yu

In this paper, we determine the $L^{p} (R) \times L^{q} (R) \to L^{r} (R)$ boundedness of the bilinear Hilbert transform $H_{γ} (f, g)$ along a convex curve $γ$ …

math.CA2019

Convergence of a Class of Schrödinger Equations

Dan Li, Haixia Yu

In this paper, we set up the selection conditions for time series ${t_{k}}_{k = 1}^{\infty}$ which converge to 0 as $k \to \infty$ such that the solutions of a class of generaliz…

math.CA2018

$L^{2}$ Boundedness of Hilbert Transforms along Variable Flat Curves

Junfeng Li, Haixia Yu

In this paper, the $L^{2}$ boundedness of the Hilbert transform along variable flat curve $(t, P (x_{1}) γ (t))$ $$H_{P,γ}f(x_1,x_2):=\mathrm{p.\,v.}\int_{-\infty}^{\infty}f(x_1-t,x_2-P(x_…

math.CA2018★ 1 cited

$L^{p}$ Boundedness of Hilbert Transforms Associated with Variable Plane Curves

Haixia Yu, Junfeng Li

Let $p \in (1, \infty)$ . In this paper, for any given measurable function $u : R \to R$ and a generalized plane curve $γ$ satisfying some conditions, the $L^…

Mixed norm estimates for dilated averages over planar curves

The Boundedness of the Bilinear Fractional Integrals along Curves

Lxp​→Lx,uq​ estimates for dilated averages over planar curves