论文标题
全体形态Hörmander-type功能性积分在扇区和条上
Holomorphic Hörmander-Type Functional Calculus on Sectors and Strips
论文作者
论文摘要
在本文中，Kriegler and Weis（2018）的最新抽象乘数定理以$ 0 $ - 部门和$ 0 $ - 斯特的类型运营商进行了完善，并概括为任意部门和脱衣舞式运营商。为此，引入了霍尔曼型霍曼德型功能，并带有比经典多项式的平滑度更细的平滑度。此外，我们对涉及Schwartz和“ Holomorphic Schwartz”功能的这些空间建立了替代描述。最后，抽象的结果与Carbonaro和Dragičević（2017）的最新结果结合在一起，以获得已知的Hörmander-type乘数定理的一般对称性收缩半群的改善 - 相对于平滑度条件 - 相对于平滑度条件得到了改进。
In this paper, recent abstract multiplier theorems for $0$-sectorial and $0$-strip type operators by Kriegler and Weis (2018) are refined and generalized to arbitrary sectorial and strip-type operators. To this end, holomorphic Hörmander-type functions on sectors and strips are introduced with a scale of smoothness being finer than the classical polynomial one. Moreover, we establish alternative descriptions of these spaces involving Schwartz and "holomorphic Schwartz" functions. Finally, the abstract results are combined with a recent result by Carbonaro and Dragičević (2017) to obtain an improvement -- with respect to the smoothness condition -- of the known Hörmander-type multiplier theorem for general symmetric contraction semigroups.
