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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.
Miroslav Krbec, and Hans-Jürgen Schmeisser. "Critical imbeddings with multivariate rearrangements." Studia Mathematica 181.3 (2007): 255-284. <http://eudml.org/doc/285085>.
@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 -