arXiv subjects

Longfa Sun

Publications and source records attributed to Longfa Sun.

3 recordsLinked to original sources

arXiv2026

The Optimal Scaling Parameter in Metric Cotype for Alexandrov Spaces of Nonnegative Curvature

We determine the optimal order of the scaling parameter in the metric cotype $2$ inequality for complete Alexandrov spaces of nonnegative curvature. It grows linearly with the dimension $n$ of the discrete torus. This answers Question 17 of Eskenazis, Mendel, and Naor. In their sign-vector normalization on $\bigl(\mathbb{Z}/(2m\mathbb{Z})\bigr)^n$, the square of the optimal metric cotype $2$ constant for this class lies between $\max\{1,n/m\}$ and $e\lceil n/m\rceil$ for every dyadic $m\geq 2$. The upper bound follows from a dyadic Bernoulli-thinning argument using only the Lang--Schroeder--Sturm inequality. Snowflake universality of the fixed Wasserstein space $\mathcal{P}_2(\mathbb{R}^3)$ gives the $n/m$ lower bound.

math.FA↗

arXiv2026

Hypercontractivity for a family of quantum Ornstein-Uhlenbeck semigroups

We show that a family of quantum Ornstein-Uhlenbeck semigroups is hypercontractive. We also obtain the optimal order of the optimal time up to a constant for those elements whose Gibbs state is zero. The main ingredient of our proof is Meixiner polynomials.

math.FA↗

arXiv2020

On the sum of simultaneously proximinal sets

In this paper, we show that the sum of a compact convex subset and a simultaneously $\tau$-strongly proximinal convex subset (resp. simultaneously approximatively $\tau$-compact convex subset) of a Banach space X is simultaneously tau-strongly proximinal (resp. simultaneously approximatively $\tau$-compact ), and the sum of weakly compact convex subset and a simultaneously approximatively weakly compact convex subset of X is still simultaneously approximatively weakly compact, where $\tau$ is the norm or the weak topology. Moreover, some related results on the sum of simultaneously proximinal subspaces are presented.

math.FA↗