Critical imbeddings with multivariate rearrangements

• Autorzy: Miroslav Krbec , Hans-Jürgen Schmeisser
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 42B35: Function spaces arising in harmonic analysis
• 46E30: Spaces of measurable functions ( L p -spaces, Orlicz spaces, K\"othe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
• 46E35: Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2007
• Tom: 181
• Numer: 3
• Strony: 255-284

Daty

wydano

2007

Twórcy

autor

Miroslav Krbec

• Institute of Mathematics, Academy of Sciences of the Czech Republic, Žitná 25, 115 67 Praha 1, Czech Republic

autor

Hans-Jürgen Schmeisser

• Mathematisches Institut, Fakultät für Mathematik und Informatik, Friedrich-Schiller-Universität, Ernst-Abbe-Platz 1-2, 07743 Jena, Germany

Identyfikatory

DOI

10.4064/sm181-3-4