从图像二分法到Haagerup不等式
From a dichotomy for images to Haagerup's inequality
摘要：
设X是紧拓扑空间，D是X的子集.设Y是Hausdorff拓扑空间。设f是D到Y的闭包的连续映射，使得f（D）是开的。设E是D的边界的补（到Y）的任何连通子集。则f（D）要么包含E，要么包含在E的补数中。应用二分法的原则，特别是全纯映射，包括最大和最小模的原则，逆边界对应，并证明Haagerup的不等式的绝对功率矩的线性组合的独立Rademacher随机变量。
英文摘要：
Let X be a compact topological space, and let D be a subset of X. Let Y be a Hausdorff topological space. Let f be a continuous map of the closure of D to Y such that f(D) is open. Let E be any connected subset of the complement (to Y) of the boundary of D. Then f(D) either contains E or is contained in the complement of E. Applications of this dichotomy principle are given, in particular for holomorphic maps, including maximum and minimum modulus principles, an inverse boundary correspondence, and a proof of Haagerup's inequality for the absolute power moments of linear combinations of independent Rademacher random variables.
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