Extension of C<SUP><i>m</i>,ω</SUP>-Smooth Functions by Linear Operators

作     者：Fefferman, Charles 

作者机构：Princeton Univ Dept Math Princeton NJ 08544 USA 

出 版 物：《REVISTA MATEMATICA IBEROAMERICANA》 (Rev. Mat. Iberoam.)

年 卷 期：2009年第25卷第1期

页      面：1-48页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

主　　题：Whitney extension problem linear operators modulus of continuity Whitney convexity 

摘      要：Let C-m,C-omega(R-n) be the space of functions on R-n whose m(th) derivatives have modulus of continuity w. For E subset of R-n, let C-m,C-omega(E) be the space of all restrictions to E of functions in C-m,C-omega(R-n). We show that there exists a bounded linear operator T : C-m,C-omega(E) - C-m,C-omega(R-n) such that, for any f is an element of C-m,C-omega (E), we have Tf = f on E.