A NOTE ON SOBOLEV TYPE TRACE INEQUALITIES FOR s-HARMONIC EXTENSIONS

被引：0

作者：

Tang, Yongrui ^{[1
]}

Zhou, Shujuan ^{[1
]}

机构：

[1] Qingdao Univ, Sch Math & Stat, Qingdao 266071, Shandong, Peoples R China

来源：

JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY | 2024年 / 61卷 / 02期

基金：

中国国家自然科学基金;

关键词：

Sobolev trace inequalities; Besov spaces; fractional Poisson ker- nels; Hardy inequalities; EQUATIONS; SPACES;

D O I：

10.4134/JKMS.j230246

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, apply the regularities of the fractional Poisson kernels, we establish the Sobolev type trace inequalities of homogeneous Besov spaces, which are invariant under the conformal transforms. Also, by the aid of the Carleson measure characterizations of Q type spaces, the local version of Sobolev trace inequalities are obtained.

引用

页码：341 / 356

页数：16

共 17 条

[1] SHARP SOBOLEV INEQUALITIES ON THE SPHERE AND THE MOSER-TRUDINGER INEQUALITY [J].

BECKNER, W .

ANNALS OF MATHEMATICS, 1993, 138 (01) :213-242

[2]

Bui HQ, 2017, CONTEMP MATH, V693, P109, DOI 10.1090/conm/693/13935

[3] An extension problem related to the fractional Laplacian [J].

Caffarelli, Luis ;

Silvestre, Luis .

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2007, 32 (7-9) :1245-1260

[4] Regularity estimates for the solution and the free boundary of the obstacle problem for the fractional Laplacian [J].

Caffarelli, Luis A. ;

Salsa, Sandro ;

Silvestre, Luis .

INVENTIONES MATHEMATICAE, 2008, 171 (02) :425-461

[5] Fractional elliptic equations, Caccioppoli estimates and regularity [J].

Caffarelli, Luis A. ;

Stinga, Pablo Raul .

ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 2016, 33 (03) :767-807

[6]

Caffarelli LA, 2010, ANN MATH, V171, P1903

[7] Some new tent spaces and duality theorems for fractional Carleson measures and Qα(Rn) [J].

Dafni, G ;

Xiao, J .

JOURNAL OF FUNCTIONAL ANALYSIS, 2004, 208 (02) :377-422

[8] Hitchhiker's guide to the fractional Sobolev spaces [J].

Di Nezza, Eleonora ;

Palatucci, Giampiero ;

Valdinoci, Enrico .

BULLETIN DES SCIENCES MATHEMATIQUES, 2012, 136 (05) :521-573

[9] SHARP CONSTANT IN A SOBOLEV TRACE INEQUALITY [J].

ESCOBAR, JF .

INDIANA UNIVERSITY MATHEMATICS JOURNAL, 1988, 37 (03) :687-698

[10] Non-linear ground state representations and sharp Hardy inequalities [J].

Frank, Rupert L. ;

Seiringer, Robert .

JOURNAL OF FUNCTIONAL ANALYSIS, 2008, 255 (12) :3407-3430

← 1 2 →