Optimal dimension-dependent ${\ell }^p$ and ${\ell }^{1,\infty }$ estimates of the discrete Riesz Transforms

Junjie Shao, Hanli Tang, Zewei Xu

In this paper, we are concerned with the optimal dimension-dependent ${\ell }^p$ norm of the discrete Riesz Transforms $R_{\text{dis}}^{(k)}$ on ${\mathbb{Z}}^d$ given by the singular c…