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)(?).
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）（？）.
基金
supported by the project "Smoothness Morrey spaces with variable exponents" approved under the agreement "Projektbezogener Personenaustausch mit Portugal-Acoes Integradas Luso-Alems’/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)
