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Acta Mathematica Sinica, English Series

, Volume 32, Issue 2, pp 137–152 | Cite as

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

  • Dorothee D. HaroskeEmail author
  • Susana D. Moura
Article

Abstract

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.

Keywords

Besov-type space Morrey space Besov–Morrey space Triebel–Lizorkin–Morrey space growth envelope atomic decomposition 

MR(2010) Subject Classification

46E35 42B35 

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Copyright information

© Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Institute of MathematicsFriedrich-Schiller-University JenaJenaGermany

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