We study smoothness spaces of Morrey type on Rn and characterise in detail those situations when such spaces of type A_(p,q)^(s,r)(R^n) or A_(u,p,q)~s(R^n) are not embedded into L_(∞)(R^n).We can show that in the so-...We study smoothness spaces of Morrey type on Rn and characterise in detail those situations when such spaces of type A_(p,q)^(s,r)(R^n) or A_(u,p,q)~s(R^n) are not embedded into L_(∞)(R^n).We can show that in the so-called sub-critical,proper Morrey case their growth envelope function is always infinite which is a much stronger assertion.The same applies for the Morrey spaces M_(u,p)(R^m) with p < u.This is the first result in this direction and essentially contributes to a better understanding of the structure of the above spaces.展开更多
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 obtain...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)(?).展开更多
基金partially supported by the Centre for Mathematics of the University of Coimbrathe European Regional Development Fund program COMPETEthe Portuguese Government through the FCT-Fundao para a Ciencia e Tecnologia under the project PEst-C/MAT/UI0324/2013
文摘We study smoothness spaces of Morrey type on Rn and characterise in detail those situations when such spaces of type A_(p,q)^(s,r)(R^n) or A_(u,p,q)~s(R^n) are not embedded into L_(∞)(R^n).We can show that in the so-called sub-critical,proper Morrey case their growth envelope function is always infinite which is a much stronger assertion.The same applies for the Morrey spaces M_(u,p)(R^m) with p < u.This is the first result in this direction and essentially contributes to a better understanding of the structure of the above spaces.
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)+1 种基金funded by the Portuguese Government through FCT/MEC and co-funded by the European Regional Development Fund through the Partnership Agreement PT2020National Science Center of Poland (Grant No. 2014/15/B/ST1/00164)
文摘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)(?).
