FUNCTIONAL CALCULUS FOR C0-GROUPS USING TYPE AND COTYPE

被引:2
|
作者
Rozendaal, Jan [1 ,2 ]
机构
[1] Australian Natl Univ, Inst Math Sci, Acton, ACT 2601, Australia
[2] Polish Acad Sci, Inst Math, Ul Sniadeckich 8, PL-00656 Warsaw, Poland
来源
QUARTERLY JOURNAL OF MATHEMATICS | 2019年 / 70卷 / 01期
关键词
FOURIER MULTIPLIER THEOREMS; REAL INTERPOLATION SPACES; RATIONAL-APPROXIMATIONS; BESOV-SPACES; SEMIGROUPS; CONVERGENCE; GENERATORS; OPERATORS; EQUATIONS;
D O I
10.1093/qmath/hay032
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
We study the functional calculus properties of generators of C-0-groups under type and cotype assumptions on the underlying Banach space. In particular, we show the following. Let - iA generate a C-0-group on a Banach space X with type p is an element of [1, 2] and cotype q is an element of [2, infinity). Then f (A): (X, D (A))(1/p -1/q,1) -> X is bounded for each bounded holomorphic function f on a p sufficiently large strip. As a corollary of this result, for sectorial operators, we quantify the gap between bounded imaginary powers and a bounded H-infinity-calculus in terms of the type and the cotype of the underlying Banach space. For cosine functions, we obtain similar results as for C-0-groups. We extend our theorems to R-bounded operator-valued calculi, and we give an application to the theory of rational approximation of C-0-groups.
引用
收藏
页码:17 / 47
页数:31
相关论文
共 50 条