Optimal dimension-dependent $\ell^p$ and $\ell^{1,\infty}$ estimates of the second-order discrete Riesz transforms
Year: 2026
Type: preprint
Abstract: In this paper we investigate the optimal dimension-dependent estimates of the second-order discrete Riesz transforms \[ R_{\mathrm{dis}}^{(jk)}f(n) = c_d\sum_{m\in\mathbb Z^d\setminus\{0\}} \frac{m_jm_k}{|m|^{d+2}}f(n-m), \qquad c_d=\frac{Γ\left(\frac{d+2}{2}\right)}{π^{d/2}}. \] For $j\neq k$ and every fixed $1
Source: arXiv (Cornell University)
Authors: Tang, Hanli, Xu, Zewei
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: G5707991678
OpenAlex ID: W7212164164