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

Advances in Pure Mathematics 2019年第2期9卷 164-204页

作者： Simon Joseph Ahmed Sufyan Hala Taha ranya tahir Department of Mathematics College of Education Dr. John Garang Memorial University of Science and Technology Bor South Sudan Department of Mathematics Ministry of Education Muscat Sultanate of Oman Department of Mathematics College of Science Princess Nourah bint Abdulrahman University Al-Riyadh KSA Department of Mathematics Faculty of Science Jazan University Jazan KSA

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.

关键词： Transference Operator Semigroup Functional Calculus Analytic Besov Peller γ-Boundedness γ-Radonifying γ-Summing Power-Bounded Operator

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