Unboundedness properties of smoothness Morrey spaces of regular distributions on domains

被引：0
作者：
Dorothee D. Haroske
Susana D. Moura
Cornelia Schneider
Leszek Skrzypczak
机构：
[1] Friedrich Schiller University Jena,Institute of Mathematics
[2] University of Coimbra,CMUC, Department of Mathematics
[3] Friedrich-Alexander University Erlangen-Nüremberg,Mathematics Department
[4] Adam Mickiewicz University,Faculty of Mathematics and Computer Science
来源：
Science China Mathematics | 2017年 / 60卷
关键词：
Morrey spaces; Besov spaces; Triebel-Lizorkin spaces; growth envelopes; atomic decompositions; inequalities; 46E35; 47B06;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We study unboundedness of smoothness Morrey spaces on bounded domains Ω ⊂ Rn in terms of growth envelopes. It turns out that in this situation the growth envelope function is finite—in contrast to the results obtained by Haroske et al. (2016) for corresponding spaces defined on Rn. A similar effect was already observed by Haroske et al. (2017), where classical Morrey spaces Mu,p(Ω) were investigated. We deal with all cases where the concept is reasonable and also include the tricky limiting cases. Our results can be reformulated in terms of optimal embeddings into the scale of Lorentz spaces Lp,q(Ω).
引用
收藏
页码：2349 / 2376
页数：27
相关论文
共 56 条
[1]  
Caetano A(1998)About approximation numbers in function spaces J Approx Theory 94 383-395
[2]  
El Baraka A(2002)An embedding theorem for Campanato spaces Electron J Differential Equations 66 1-17
[3]  
El Baraka A(2006)Littlewood-Paley characterization for Campanato spaces J Funct Spaces Appl 4 193-220
[4]  
Haroske D D(2016)Some specific unboundedness property in smoothness Morrey spaces: The non-existence of growth envelopes in the subcritical case Acta Math Sin (Engl Ser) 32 137-152
[5]  
Moura S D(2016)Smoothness Morrey spaces of regular distributions, and some unboundedness properties Nonlinear Anal 139 218-244
[6]  
Haroske D D(2012)Continuous embeddings of Besov-Morrey function spaces Acta Math Sin (Engl Ser) 28 1307-1328
[7]  
Moura S D(2013)Embeddings of Besov-Morrey spaces on bounded domains Studia Math 218 119-144
[8]  
Skrzypczak L(2014)On Sobolev and Franke-Jawerth embeddings of smoothness Morrey spaces Rev Mat Complut 27 541-573
[9]  
Haroske D D(1994)Semilinear heat equations and the Navier-Stokes equation with distributions in new function spaces as initial data Comm Partial Differential Equations 19 959-1014
[10]  
Skrzypczak L(2003)Besov-Morrey spaces: Function space theory and applications to non-linear PDE Trans Amer Math Soc 355 1297-1364
123456