1 citations · 1 across the 13 of their papers we have counts for
13 papers
Optimal dimension-dependent and estimates of the second-order discrete Riesz transforms
Hanli Tang, Zewei Xu
In this paper we investigate the optimal dimension-dependent estimates of the second-order discrete Riesz transforms \[ R_{\mathrm{dis}}^{(jk)}f(n) = c_d\sum_{m\in\mathbb Z^d\setmi…
Sharp constants for weak estimates of the Riesz Potentials
Hanli Tang, Yaojun Wang
In this paper we prove the sharp weak estimates for the Riesz potentials $$\|I_{s}(f)\|_{L^{\frac{n}{n-s},\infty}}\leq γ_{n,s} v_n^{\frac{n-s}{n}}\frac{Γ(s/2)Γ((n+2-s)/2)}{Γ(n/2)}\…
Optimal dimension-dependent and estimates of the discrete Riesz Transforms
Junjie Shao, Hanli Tang, Zewei Xu
In this paper, we are concerned with the optimal dimension-dependent norm of the discrete Riesz Transforms on given by the singular c…
Stability for Critical Points of the Hardy--Littlewood--Sobolev Inequality and a Dual Stability Framework
Lu Chen, Guozhen Lu, Hanli Tang
Although quantitative stability for critical points of the Sobolev and fractional Sobolev inequalities has been extensively studied, the corresponding stability theory for critical…
Asymptotically sharp stability of Sobolev inequalities on the Heisenberg group with dimension-dependent constants
Lu Chen, Guozhen Lu, Hanli Tang +1
In this paper, we are concerned with the optimal asymptotic lower bound for the stability of Sobolev inequality on the Heisenberg group. We first establish the optimal local stabil…
Optimal stability of Hardy-Littlewood-Sobolev and Sobolev inequalities of arbitrary orders with dimension-dependent constants
Lu Chen, Guozhen Lu, Hanli Tang
Recently, Dolbeault-Esteban-Figalli-Frank-Loss [20] established the optimal stability of the first-order -Sobolev inequality with dimension-dependent constant. Subsequently, C…
Optimal asymptotic lower bound for stability of fractional Sobolev inequality and the stability of Log-Sobolev inequality on the sphere
Lu Chen, Guozhen Lu, Hanli Tang
We establish the optimal asymptotic lower bound for the stability of fractional Sobolev inequality: \begin{equation}\label{Sob sta ine} \left\|(-Δ)^{s/2} U \right\|_2^2 - \mathcal…
Stability of Hardy-Littlewood-Sobolev inequalities with explicit lower bounds
Lu Chen, Guozhen Lu, Hanli Tang
In this paper, we establish the stability for the Hardy-Littlewood-Sobolev (HLS) inequalities with explicit lower bounds. By establishing the relation between the stability of HLS…
Sharp Stability of Log-Sobolev and Moser-Onofri inequalities on the Sphere
Lu Chen, Guozhen Lu, Hanli Tang
In this paper, we are concerned with the stability problem for endpoint conformally invariant cases of the Sobolev inequality on the sphere . Namely, we will establis…
Optimal weak estimates for Riesz potentials
Liang Huang, Hanli Tang
In this note we prove a sharp reverse weak estimate for Riesz potentials $$\|I_{s}(f)\|_{L^{\frac{n}{n-s},\infty}}\geq γ_sv_{n}^{\frac{n-s}{n}}\|f\|_{L^1}~~\text{for}~~0<f\in {L^1(…
Reverse conformally invariant Sobolev inequalities on the sphere
Rupert L. Frank, Tobias König, Hanli Tang
We consider the optimization problem corresponding to the sharp constant in a conformally invariant Sobolev inequality on the -sphere involving an operator of order . In…
Classification of solutions of an equation related to a conformal log Sobolev inequality
Rupert L. Frank, Tobias König, Hanli Tang
We classify all finite energy solutions of an equation which arises as the Euler--Lagrange equation of a conformally invariant logarithmic Sobolev inequality on the sphere due to B…
On the bounds of sharp Trudinger-Moser inequalities
Hanli Tang
In this paper, we establish the bounds of sharp Trudinger-Moser inequalities on Euclidean space. Let be a ball in and $$TM(B)=\sup_{u\in{W_{0}^{1,n}(B)},\|\nabla…