H∞-calculus for semigroup generators on BMO
H∞-calculus for semigroup generators on BMO
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DOI：
10.1016/j.aim.2019.02.027
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发表时间：
2017-01
影响因子：
1.7
通讯作者：
T. Ferguson;T. Mei;Brian Simanek
中科院分区：
文献类型：
--
作者：
T. Ferguson;T. Mei;Brian Simanek
证明了L∞上正压缩半群的负生成元L在Poisson半群-BMO空间上有界H∞（S η）-演算，只要L满足Bakry-Émery的Γ 2≥ 0准则.我们的论点只依赖于基础半群的性质，并在非交换设置工作得很好。本文的一个关键内容是从属半群T t，α= e− tL α，0< α< 1的一类拟单调性质，这在本文的第一部分中得到了证明。
We prove that the negative generator L of a semigroup of positive contractions on L∞ has bounded H∞(S η)-calculus on the associated Poisson semigroup-BMO space for any angle η> π/2, provided L satisfies Bakry-Émery's Γ 2≥ 0 criterion. Our arguments only rely on the properties of the underlying semigroup and work well in the noncommutative setting. A key ingredient of our argument is a type of quasi monotone properties for the subordinated semigroup T t, α= e− t L α, 0< α< 1, that is proved in the first part of this article.