Unboundedness properties of smoothness Morrey spaces of regular distributions on domains

作     者：HAROSKE Dorothee D. MOURA Susana D. SCHNEIDER Cornelia SKRZYPCZAK Leszek 

作者机构：Institute of Mathematics Friedrich Schiller University Jena CMUC Department of Mathematics University of Coimbra Mathematics Department Friedrich-Alexander University Erlangen-Nremberg Faculty of Mathematics and Computer Science Adam Mickiewicz University 

出 版 物：《Science China Mathematics》 (中国科学：数学（英文版）)

年 卷 期：2017年第60卷第12期

页      面：2349-2376页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：supported by the project "Smoothness Morrey spaces with variable exponents" approved under the agreement "Projektbezogener Personenaustausch mit Portugal-Acoes Integradas Luso-Alems’/DAAD-CRUP" the Centre for Mathematics of the University of Coimbra (Grant No. UID/MAT/00324/2013) funded by the Portuguese Government through FCT/MEC and co-funded by the European Regional Development Fund through the Partnership Agreement PT2020 National Science Center of Poland (Grant No. 2014/15/B/ST1/00164) 

主　　题：Morrey spaces Besov spaces Triebel-Lizorkin spaces growth envelopes atomic decompositions inequalities 

摘      要：We study unboundedness of smoothness Morrey spaces on bounded domains ? ? R^n 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 R^n. A similar effect was already observed by Haroske et al.(2017), where classical Morrey spaces M_(u,p)(?) 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 L_(p,q)(?).