Bo Xiang

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math.FA2026

Sphere version of Banach--Kadec--Paley theorem

Qingjin Cheng, Wuyi He, Bo Xiang

We introduce the notion of almost Lipschitz embeddings between metric spaces and apply it to the quantitative geometry of unit spheres of classical $L_p$-spaces. Our main result…

math.FA2026

Sharp Metric Cotype Inequalities for $L_{1}$ via Nonlinear Cut Smoothing

Qingjin Cheng, Yue Wang, Bo Xiang

For every $1 \leq p < \infty$ and even integer $m \geq 4$ , we determine the optimal order of the $p$ -moment torus inequality for $L_{1}$ : it is $m^{p} n^{(1 - p /2)_{+}} + n$ , with comparison cons…

Sphere version of Banach--Kadec--Paley theorem

Sharp Metric Cotype Inequalities for L1​ via Nonlinear Cut Smoothing

Sharp Metric Cotype Inequalities for $L_{1}$ via Nonlinear Cut Smoothing