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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…