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
A necessary and sufficient condition for the generalized shift operator T = S-k - (a(1)((1)), a(2)((1)),...) x e(1) - ... -(a(1)((j)), a(2)((j)),...) x e(j) (j greater than or equal to k) on l(1) to be power bounded i...A necessary and sufficient condition for the generalized shift operator T = S-k - (a(1)((1)), a(2)((1)),...) x e(1) - ... -(a(1)((j)), a(2)((j)),...) x e(j) (j greater than or equal to k) on l(1) to be power bounded is obtained. Moreover,this note points out that the power bounded operator T = S - (1, 1,...) x c(1) can shift a basis of [e(j+1) - e(j)](j = 1)(infinity), and this basis is not equivalent to {T(n)e(1)} (infinity)(n=0).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 Education DepartmentFoundation of Henan province.
文摘A necessary and sufficient condition for the generalized shift operator T = S-k - (a(1)((1)), a(2)((1)),...) x e(1) - ... -(a(1)((j)), a(2)((j)),...) x e(j) (j greater than or equal to k) on l(1) to be power bounded is obtained. Moreover,this note points out that the power bounded operator T = S - (1, 1,...) x c(1) can shift a basis of [e(j+1) - e(j)](j = 1)(infinity), and this basis is not equivalent to {T(n)e(1)} (infinity)(n=0).
