Sharp Estimates of the Norms of Embeddings between Besov Spaces

被引:2
作者
Dominguez, Oscar [1 ]
机构
[1] Univ Complutense Madrid, Fac Matemat, Dept Anal Matemat & Matemat Aplicada, Plaza Ciencias 3, E-28040 Madrid, Spain
来源
ZEITSCHRIFT FUR ANALYSIS UND IHRE ANWENDUNGEN | 2018年 / 37卷 / 02期
关键词
Besov spaces; embedding norms; interpolation; Lipschitz spaces; LIMITING EMBEDDINGS; REAL INTERPOLATION; SMOOTHNESS; THEOREMS;
D O I
10.4171/ZAA/1606
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
Optimal estimates are obtained for the rates of blow up of the norm of the embedding B-p,r(s) -> B-q,r(s-n(1/p) (-) (1/q)) with p < q as s -> n(1/p - 1-q)+. We also show optimal limiting embeddings between Besov spaces and Lipschitz spaces.
引用
收藏
页码:127 / 149
页数:23
相关论文
共 42 条
[1]   INTEGRABILITY THEOREMS FOR FOURIER SERIES [J].
ASKEY, R ;
WAINGER, S .
DUKE MATHEMATICAL JOURNAL, 1966, 33 (01) :223-&
[2]  
Bennett C., 1988, Interpolation of operators
[3]  
Bergh J., 1976, Interpolation spaces. An introduction
[4]   On spaces of functions of smoothness zero [J].
Besov, O. V. .
SBORNIK MATHEMATICS, 2012, 203 (08) :1077-1090
[5]  
Besov O. V., 1979, INTEGRAL REPRESENTAT, V1
[6]  
Besov O. V., 1979, Integral representations of functions and imbedding theorems, VII
[7]   Limiting embedding theorems for Ws,p,p when s ↑ 1 and applications [J].
Bourgain, J ;
Brezis, H ;
Mironescu, P .
JOURNAL D ANALYSE MATHEMATIQUE, 2002, 87 (1) :77-101
[8]  
Bourgain J, 2001, OPTIMAL CONTROL AND PARTIAL DIFFERENTIAL EQUATIONS, P439
[9]  
Brudnyi Y., 1991, INTERPOLATION FUNCTO, V1
[10]  
Cobos F., 2015, COMMENT MATH HELV, V55, P79