Some specific unboundedness property in smoothness Morrey spaces. The non-existence of growth envelopes in the subcritical case

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• 作者：Dorothee D. Haroske ; Susana D. Moura
• 关键词：Besov ; type space ; Morrey space ; Besov–Morrey space ; Triebel–Lizorkin–Morrey space ; growth envelope ; atomic decomposition
• 刊名：Acta Mathematica Sinica
• 出版年：2016
• 出版时间：February 2016
• 年：2016
• 卷：32
• 期：2
• 页码：137-152
• 全文大小：271 KB
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• 作者单位：Dorothee D. Haroske (1)
  Susana D. Moura (1)
  
  1. Institute of Mathematics, Friedrich-Schiller-University Jena, 07737, Jena, Germany
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  Chinese Library of Science
  
• 出版者：Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society, co-published
• ISSN：1439-7617

文摘

We study smoothness spaces of Morrey type on R n and characterise in detail those situations when such spaces of type A _p,q s,τ (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 n ) 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.