Critical imbeddings with multivariate rearrangements

@article{MiroslavKrbec2007,
abstract = {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.},
author = {Miroslav Krbec, Hans-Jürgen Schmeisser},
journal = {Studia Mathematica},
keywords = {limiting embeddings; dominating mixed derivatives; Besov spaces; Triebel-Lizorkin spaces; Lorentz-Orlicz spaces},
language = {eng},
number = {3},
pages = {255-284},
title = {Critical imbeddings with multivariate rearrangements},
url = {http://eudml.org/doc/285085},
volume = {181},
year = {2007},
}

TY - JOUR
AU - Miroslav Krbec
AU - Hans-Jürgen Schmeisser
TI - Critical imbeddings with multivariate rearrangements
JO - Studia Mathematica
PY - 2007
VL - 181
IS - 3
SP - 255
EP - 284
AB - 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.
LA - eng
KW - limiting embeddings; dominating mixed derivatives; Besov spaces; Triebel-Lizorkin spaces; Lorentz-Orlicz spaces
UR - http://eudml.org/doc/285085
ER -