On limiting embeddings of Besov spaces

• Autorzy: V. I. Kolyada , A. K. Lerner
• Języki publikacji: EN

Abstrakty

EN

We investigate the classical embedding $B_{p,θ}^{s} ⊂ B_{q,θ}^{s-n(1/p-1/q)}$. The sharp asymptotic behaviour as s → 1 of the operator norm of this embedding is found. In particular, our result yields a refinement of the Bourgain, Brezis and Mironescu theorem concerning an analogous problem for the Sobolev-type embedding. We also give a different, elementary proof of the latter theorem.

Kategorie tematyczne

• 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: 2005
• Tom: 171
• Numer: 1
• Strony: 1-13

Daty

wydano

2005

Twórcy

autor

V. I. Kolyada

• Department of Mathematics, Karlstad University, 651 88 Karlstad, Sweden

autor

A. K. Lerner

• Department of Mathematics, Bar-Ilan University, 52900 Ramat Gan, Israel

Identyfikatory

DOI

10.4064/sm171-1-1