Author

Zhou-Yu Long

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Preprint Oct 2026

Sharp noncommutative Hilbert and Riesz inequalities: classification and spectral corrections

For every $1<p<\infty$, with $p^*=\max\{p,p/(p-1)\}$, we determine the sharp Hilbert norm $C_p=\cot(\pi/(2p^*))$ on $L^p(\mathbb{R};\mathcal{S}_p)$ and the sharp uniform bound $D_p=\csc(\pi/p)$ for retained and strict Riesz projections of maximal subdiagonal algebras in finite tracial von Neumann algebras. The Hilbert...

Zhou-Yu Long · 0 citations

Preprint Oct 2026

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...

Zhou-Yu Long · 0 citations