Zhou-Yu Long

Sharp Hilbert transform norms on Schatten classes: classification and optimal spectral corrections

For every $1<p<\infty$, the Hilbert transform on $L^p(\mathbb{R};\mathcal{S}_p)$ and the ordered Hilbert Schur multiplier on $\mathcal{S}_p$ have norm $C_p=\cot(\pi/(2p^*))$, where $p^*=\max\{p,p/(p-1)\}$. The scalar Hilbert transform and the Schur multiplier have the same canonical completely bounded norm. This proves...