4 papers · 1 filter
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 $$\|I_{s}(f)\|_{L^{\frac{n}{n-s},\infty}}\leq γ_{n,s} v_n^{\frac{n-s}{n}}\frac{Γ(s/2)Γ((n+2-s)/2)}{Γ(n/2)}\…
Optimal dimension-dependent and estimates of the discrete Riesz Transforms
Junjie Shao, Hanli Tang, Zewei Xu
In this paper, we are concerned with the optimal dimension-dependent norm of the discrete Riesz Transforms on given by the singular c…
Optimal weak estimates for Riesz potentials
Liang Huang, Hanli Tang
In this note we prove a sharp reverse weak estimate for Riesz potentials $$\|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(…