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 ...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.展开更多
In this article, we consider compound matrices and compound operator equations in a Hilbert space. First, we recall some concepts and main results introduced by Muldowney and by Roger Temam. After that we establish th...In this article, we consider compound matrices and compound operator equations in a Hilbert space. First, we recall some concepts and main results introduced by Muldowney and by Roger Temam. After that we establish the rule of compound matrices in a Hilbert space, and obtain the expression of solution to a compound operator equation by using the method of operator semigroup. Our brief results generalize the corresponding results in a finite space.展开更多
文摘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.
基金The NNSF (10171010 and 10201005) of China Major Project of Education Ministry (01061) of China.
文摘In this article, we consider compound matrices and compound operator equations in a Hilbert space. First, we recall some concepts and main results introduced by Muldowney and by Roger Temam. After that we establish the rule of compound matrices in a Hilbert space, and obtain the expression of solution to a compound operator equation by using the method of operator semigroup. Our brief results generalize the corresponding results in a finite space.
