Notes on Spaces of Functions Converging at Infinity

A note on one-dimensional Poincaré inequalities by Stein-type integration

We study the weighted Poincaré constant $C(p,w)$ of a probability density $p$ with weight function $w$ using integration methods inspired by Stein's method. We obtain a new version of the Chen-Wang variational formula which, as a byproduct, yields simple upper and lower bounds on $C(p,w)$ in terms of the so-called Stein kernel of $p$. We also iterate these variational formulas so as to build sequences of nested intervals containing the Poincaré constant, sequences of functions converging to said constant, as well as sequences of functions converging to the solutions of the corresponding spectr…

H-infinity与复插值

H-infinity and Complex Interpolation

本研究是对1981年Jaak Peetre关于H-infinity与复插值的隆德技术报告的精确复刻，补充了近年参考文献、更新部分文献并修正印刷错误。

A note on the weak* and pointwise convergence of BV functions

We study pointwise convergence properties of weakly* converging sequences $\{u_i\}_{i \in {\mathbb N}}$ in $\mathrm{BV}({\mathbb R}^n)$. We show that, after passage to a suitable subsequence (not relabeled), we have pointwise convergence $u_i^*(x)\to u^*(x)$ of the precise representatives for all $x\in {\mathbb R}^n \setminus E$, where the exceptional set $E \subset {\mathbb R}^n$ has on the one hand Hausdorff dimension at most $n-1$, and is on the other hand also negligible with respect to the Cantor part of $|D u|$. Furthermore, we discuss the optimality of these results.

Compact endomorphisms of H infinity of D

When G is a region in the complex plane, compact composition operators on the uniform algebra of bounded analytic functions on G and the spectra of these operators were described by D. Swanton, Compact composition operators on B(D), Proc. Amer. Math. Soc. 56 (1976). In this short note we characterize all compact endomorphisms, not necessarily those induced by composition operators, on the uniform algebra of bounded analytic functions on the open unit disc, and determine their spectra. This research was supported by EPSRC grant GR/M31132

关于图适应褶皱空间的渐近锥的注记

A note on asymptotic cones of graph-adapted smocked spaces

本文引入图适应褶皱实现，证明褶皱度量与图度量间的一致加性扭曲估计，进而得出图适应褶皱保持稳定范数和渐近锥，并证明每个中心对称有理多面体范数可作为图适应褶皱空间的唯一无穷远切锥。

关于构造分析中的q-赋范空间的注记

Notes on q-normed Spaces in Constructive Analysis

本文研究构造分析中q-赋范空间的性质，证明标准定理的q-赋范空间类比/推广，并给出两个定理的类比本质上是非构造性的例子。