摘要
Abstract We study smoothness spaces of Morrey type on Rn and characterise in detail those situa s,r n s n tions when such spaces of type Ap,q^s,r（Rn ） or A u^sp,q（R ） 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 Mu,p（Rn） 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.
Abstract We study smoothness spaces of Morrey type on Rn and characterise in detail those situa s,r n s n tions when such spaces of type Ap,q^s,r（Rn ） or A u^sp,q（R ） 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 Mu,p（Rn） 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
partially supported by the Centre for Mathematics of the University of Coimbra
the European Regional Development Fund program COMPETE
the Portuguese Government through the FCT-Fundao para a Ciencia e Tecnologia under the project PEst-C/MAT/UI0324/2013
