Critical imbeddings with multivariate rearrangements

Volume 181 / 2007

Miroslav Krbec, Hans-Jürgen Schmeisser Studia Mathematica 181 (2007), 255-284 MSC: Primary 46E35; Secondary 42B35, 46E30. DOI: 10.4064/sm181-3-4


We are concerned with imbeddings of general spaces of Besov and Lizorkin–Triebel type with dominating mixed derivatives in the first critical case. We employ multivariate exponential Orlicz and Lorentz–Orlicz spaces as targets. We study basic properties of the target spaces, in particular, we compare them with usual exponential spaces, showing that in this case the multivariate clones are in fact better adapted to the character of smoothness of the imbedded spaces. Then we prove sharp limiting imbedding theorems and establish estimates for the multivariate growth envelope functions.


  • Miroslav KrbecInstitute of Mathematics
    Academy of Sciences of the Czech Republic
    Žitná 25
    115 67 Praha 1, Czech Republic
  • Hans-Jürgen SchmeisserMathematisches Institut
    Fakultät für Mathematik und Informatik
    Ernst-Abbe-Platz 1-2
    07743 Jena, Germany

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