Geodesic
Critical imbeddings with multivariate rearrangements
Miroslav Krbec1 ; Hans-Jürgen Schmeisser2
1Institute of Mathematics Academy of Sciences of the Czech Republic Žitná 25 115 67 Praha 1, Czech Republic
2Mathematisches Institut Fakultät für Mathematik und Informatik Friedrich-Schiller-Universität Ernst-Abbe-Platz 1-2 07743 Jena, Germany
Studia Mathematica, Tome 181 (2007) no. 3, pp. 255-284
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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.
DOI : 10.4064/sm181-3-4
Keywords: concerned imbeddings general spaces besov lizorkin triebel type dominating mixed derivatives first critical employ multivariate exponential orlicz lorentz orlicz spaces targets study basic properties target spaces particular compare usual exponential spaces showing multivariate clones better adapted character smoothness imbedded spaces prove sharp limiting imbedding theorems establish estimates multivariate growth envelope functions

Miroslav Krbec  1   ; Hans-Jürgen Schmeisser  2

1 Institute of Mathematics Academy of Sciences of the Czech Republic Žitná 25 115 67 Praha 1, Czech Republic
2 Mathematisches Institut Fakultät für Mathematik und Informatik Friedrich-Schiller-Universität Ernst-Abbe-Platz 1-2 07743 Jena, Germany 
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Miroslav Krbec; Hans-Jürgen Schmeisser. Critical imbeddings with multivariate rearrangements. Studia Mathematica, Tome 181 (2007) no. 3, pp. 255-284. doi: 10.4064/sm181-3-4

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