Traces of Sobolev spaces on Ahlfors sets of Carnot groups

被引：2

作者：

Vodop'yanov, S. K. ^{[1
]}

Pupyshev, I. M. ^{[1
]}

机构：

[1] Russian Acad Sci, Sobolev Inst Math, Siberian Div, Novosibirsk 630090, Russia

来源：

DOKLADY MATHEMATICS | 2006年 / 74卷 / 03期

基金：

俄罗斯基础研究基金会;

关键词：

Sobolev Space; Hausdorff Dimension; DOKLADY Mathematic; Extension Operator; Carnot Group;

D O I：

10.1134/S1064562406060044

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The traces of Sobolev spaces on Ahlfors sets of Carnot groups were analyzed. The problem of traces of Sobolve spaces was solved using Bessel potential space Lpα with 1< P < ∞ and β = α -n-d/p ∈ (0,∞)to satisfy the regularity conditions such as Ahlfors sets. The solutions of the boundary value problems of elliptic equations were used to characterize traces of Sobolev spaces on the boundary of domain in Euclidean space. It was found that theorems about traces of function space help in mathematical analysis and applications.

引用

页码：799 / 804

页数：6

共 10 条

[1]

BESOV OV, 1959, DOKL AKAD NAUK SSSR+, V126, P1163

[2]

DANIELLI D, 2002, PREPRINT

[3]

Folland G. B., 1982, Hardy spaces on homogeneous groups, V28

[4]

FOLLAND GB, 1975, ARK MAT, V13, P161, DOI 10.1007/BF02386204

[5]

JOHNSSON A, 1984, MATH REP, V2, P1

[6]

Stein E., 1971, Introduction to Fourier Analysis on Euclidean Spaces

[7]

Stein E. M., 1970, SINGULAR INTEGRALS D

[8] CHARACTERIZATION OF FUNCTIONS ARISING AS POTENTIALS .2. [J].

STEIN, EM .

BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1962, 68 (06) :577-&

[9]

[Водопьянов C.К. Vodopyanov S.K.], 2006, [Доклады Академии наук, Doklady Akademii nauk], V406, P586

[10]

Whitney H, 1934, T AM MATH SOC, V36, P63, DOI 10.2307/1989708

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