8 citations · 14 across the 17 of their papers we have counts for
20 papers
Weak type (1,1) bound criterion for maximal truncated singular integral operators with rough kernels
Xudong Lai, Lingxin Xu
This paper proves the weak type (1,1) boundedness for maximal truncated singular integral operators with rough non-convolution kernels of the form , where is hom…
Weak type boundedness of Bochner--Riesz means at the critical index on quantum tori
Xudong Lai
We establish a weak type estimate for the Bochner--Riesz mean operator at the critical index on the quantum torus , where the associated k…
Weak type boundedness of noncommutative singular integral operators with rough kernels
Xudong Lai
In this paper, we establish the weak type boundedness of noncommutative singular integral operators with rough kernels. To deal with the rough kernels, we develop some orth…
Noncommutative weak type estimates for Calderón-Zygmund operators with a class of -integral conditions
Xudong Lai, Lingxin Xu
We construct a slightly new noncommutative Calderón-Zygmund decomposition by further splitting the bad function. Using this tool, we prove the weak type (1,1) boundedness of noncom…
Weak estimate for maximal truncated rough singular integral operator
Xudong Lai
In their seminal work (Amer. J. Math. 78: 289-309, 1956), Calderón and Zygmund introduced the maximal truncated rough singular integral operator and established its -boundedne…
Noncommutative Bourgain's circular maximal theorem and a local smoothing estimate on the generalized Moyal planes
Guixiang Hong, Xudong Lai, Liang Wang
In this paper, we establish a local smoothing estimate on two-dimensional quantum Euclidean space. This is the noncommutative analogue of the one due to MockenhauptSeegerSogg…
An endpoint estimate for the maximal Calderón commutator with rough kernel
Guoen Hu, Xudong Lai, Xiangxing Tao +1
In this paper, the authors consider the endpoint estimates for the maximal Calderón commutator defined by $$T_{Ω,\,a}^*f(x)=\sup_{ε>0}\Big|\int_{|x-y|>ε}\frac{Ω(x-y)}{|x-y|^{d+1}}…
Noncommutative maximal strong estimates of Calderón-Zygmund operators
Guixiang Hong, Xudong Lai, Samya Kumar Ray +1
In this paper, we obtain the desired noncommutative maximal inequalities of the truncated Calderón-Zygmund operators of non-convolution type acting on operator-valued -functio…
Fourier restriction estimates on quantum Euclidean spaces
Guixiang Hong, Xudong Lai, Liang Wang
In this paper, we initiate the study of the Fourier restriction phenomena on quantum Euclidean spaces, and establish the analogues of the Tomas-Stein restriction theorem and the tw…
Sharp estimates of noncommutative Bochner-Riesz means on two-dimensional quantum tori
Xudong Lai
In this paper, we establish the full boundedness of noncommutative Bochner-Riesz means on two-dimensional quantum tori, which completely resolves an open problem raised in \c…
Maximal singular integral operators acting on noncommutative -spaces
Guixiang Hong, Xudong Lai, Bang Xu
In this paper, we study the boundedness theory for maximal Calderón-Zygmund operators acting on noncommutative -spaces. Our first result is a criterion for the weak type $(1,1…
Noncommutative maximal operators with rough kernels
Xudong Lai
This paper is devoted to the study of noncommutative maximal operators with rough kernels. More precisely, we prove the weak type boundedness for noncommutative maximal ope…
Maximal operator for the higher order Calderón commutator
Xudong Lai
In this paper, we investigate the weighted multilinear boundedness properties of the maximal higher order Calderón commutator for the dimensions larger than two. We establish all w…
On the composition for rough singular integral operators
Guoen Hu, Xudong Lai, Qingying Xue
In this paper, we investigate the behavior of the bounds of the composition for rough singular integral operators on the weighted space. More precisely, we obtain the quantitative…
Multilinear estimates for Calderón commutators
Xudong Lai
In this paper, we investigate the multilinear boundedness properties of the higher (-th) order Calderón commutator for dimensions larger than two. We establish all multilinear e…
Bilinear endpoint estimates for Calderón commutator with rough kernel
Xudong Lai
In this paper, we establish some bilinear endpoint estimates of Calderón commutator with a homogeneous kernel when . M…
A note on the discrete Fourier restriction problem
Xudong Lai, Yong Ding
In this paper, we establish a general discrete Fourier restriction theorem. As an application, we make some progress on the discrete Fourier restriction associated with KdV equatio…
Weak type (1,1) bound criterion for singular integral with rough kernel and its applications
Yong Ding, Xudong Lai
In this paper, a weak type (1,1) bound criterion is established for singular integral operator with rough kernel. As some applications of this criterion, we prove some important op…
-Dini conditions and limiting behavior of weak type estimates for singular integrals
Yong Ding, Xudong Lai
In 2006, Janakiraman [10] showed that if with mean value zero on satisfies the condition \[ \sup_{|ξ|=1}\int_{S^{n-1}}|Ω(θ)-Ω(θ+δξ)|dσ(θ)\leq Cnδ\int_{S^{n-1}}|Ω(θ)|d…
Weighted bound for commutators
Yong Ding, Xudong Lai
Let be the Calderón-Zygmund convolution kernel on . Define the commutator associated with and by \[ T_af(x)=p.v. \int K…