论文标题
抽象一阶差异操作员的菲利普斯微积分的界限
Bounds on the Phillips calculus of abstract first order differential operators
论文作者
论文摘要
对于在$ l^p $ spaces上生成组的操作员，转移结果给出了菲利普斯功能积分的边界，也称为光谱乘数估计。在本文中，我们考虑了特定的组发电机，这些发电机是一阶差异操作员的抽象，并证明了类似的频谱乘数估计，假设该组仅以$ l^2 $而不是$ l^p $为界。我们还通过假设sobolev嵌入属性并表明扰动的Hodge-DIRAC运算符的平方具有这样的计算，我们还通过假设Sobolev嵌入属性来证明hörmanderconculus结果。
For an operator generating a group on $L^p$ spaces transference results give bounds on the Phillips functional calculus also known as spectral multiplier estimates. In this paper we consider specific group generators which are abstraction of first order differential operators and prove similar spectral multiplier estimates assuming only that the group is bounded on $L^2$ rather than $L^p$. We also prove an R-bounded Hörmander calculus result by assuming an abstract Sobolev embedding property and show that the square of a perturbed Hodge-Dirac operator has such calculus.
