Transference Principles for the Series of Semigroups with a Theorem of Peller

A general approach to transference principles for discrete and continuous sequence of operators (semi) groups is described. This allows one to recover the classical transference results of Calderon, Coifman and Weiss and of Berkson, Gilleppie and Muhly and the more recent one of the author. The method is applied to derive a new transference principle for (discrete and continuous) the sequence of operators semigroups that need not be grouped. As an application, functional calculus estimates for bounded sequence of operators with at most polynomially growing powers are derived, leading to a new proof of classical results by Peller from 1982. The method allows for a generalization of his results away from Hilbert spaces to -spaces and—involving the concept of γ-boundedness—to general spaces. Analogous results for strongly-continuous one-parameter (semi) groups are presented as well by Markus Haase [1]. Finally, an application is given to singular integrals for one-parameter semigroups.

气－液－固三相体系颗粒完全离底悬浮的临界搅拌转速

在机械搅拌槽中，使用翼形轴流桨（Ｋ４）、涡轮桨（ＤＴ）、６叶４５°斜叶桨（６ＰＴＤ、６ＰＴＵ）（排出流向下、向上），对低粘度物系气－液－固三相体系的颗粒完全离底悬浮的临界搅拌转速Ｎ_（ＪＳＧ）作了实验研究，阐明了不同搅拌桨结构下，悬浮液浓度及通气量对Ｎ_（ＪＳＧ）的影响规律。实验得出在相同的悬浮液浓度及通气量下，Ｋ４的Ｎ_（ＪＳＧ）最低。