Interpolation Hilbert Spaces Between Sobolev Spaces

被引：20

作者：

Mikhailets, Vladimir A. ^{[1
,2
]}

Murach, Aleksandr A. ^{[1
,3
]}

机构：

[1] Natl Acad Sci Ukraine, Inst Math, UA-01601 Kiev, Ukraine

[2] Natl Tech Univ Ukraine, Kyiv Polytech Inst, Kiev, Ukraine

[3] Chernihiv Natl Pedag Univ, Chernihiv, Ukraine

来源：

RESULTS IN MATHEMATICS | 2015年 / 67卷 / 1-2期

关键词：

Sobolev space; interpolation space; Hormander space; OR-varying function; interpolation with a function parameter; FUNCTION PARAMETER; BESOV-SPACES;

D O I：

10.1007/s00025-014-0399-x

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We explicitly describe all Hilbert function spaces that are interpolation spaces with respect to a given couple of Sobolev inner product spaces considered over R-n or a half-space in R-n or a bounded Euclidean domain with Lipschitz boundary. We prove that these interpolation spaces form a subclass of isotropic Hormander spaces. They are parametrized with a radial function parameter which is OR-varying at +infinity and satisfies some additional conditions. We give explicit examples of intermediate but not interpolation spaces.

引用

页码：135 / 152

页数：18