COMPOSITION OPERATORS ON POTENTIAL SPACES

被引：31

作者：

ADAMS, DR

FRAZIER, M

机构：

[1] UNIV KENTUCKY,DEPT MATH,LEXINGTON,KY 40506

[2] WASHINGTON UNIV,DEPT MATH,ST LOUIS,MO 63130

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 1992年 / 114卷 / 01期

关键词：

SOBOLEV SPACE; POTENTIAL SPACE; COMPOSITION OPERATOR;

D O I：

10.2307/2159794

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

By a result of B. Dahlberg, the composition operators T(H)f = H degrees f need not be bounded on some of the Sobolev spaces (or spaces of Bessel potentials) even for very smooth functions H = H(t), H(0) = 0, unless of course, H(t) = ct. In this note a natural domain is found for T(H) that is, in a sense, maximal and on which the {T(H)} form an algebra of bounded operators. Here the functions H(t) need not be bounded though they are required to have a sufficient number of bounded derivatives.

引用

页码：155 / 165

页数：11

共 11 条

[1] EQUIVALENCE OF 2 DEFINITIONS OF CAPACITY [J].