On limiting embeddings of Besov spaces

V. I. Kolyada; A. K. Lerner

doi:10.4064/sm171-1-1

On limiting embeddings of Besov spaces

V. I. Kolyada
, A. K. Lerner

Department of Mathematics

Karlstad University

Research output: Contribution to journal › Article › peer-review

35 Scopus citations

Abstract

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.

Original language	English
Pages (from-to)	1-13
Number of pages	13
Journal	Studia Mathematica
Volume	171
Issue number	1
DOIs	https://doi.org/10.4064/sm171-1-1
State	Published - 2005

Keywords

Besov space
Embedding theorem
Modulus of continuity
Rearrangement estimate

Access to Document

10.4064/sm171-1-1

Cite this

@article{44c32a4c70df43b5a502910802d6c796,

title = "On limiting embeddings of Besov spaces",

abstract = "We investigate the classical embedding Bp,θs ⊂ Bq,θs-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.",

keywords = "Besov space, Embedding theorem, Modulus of continuity, Rearrangement estimate",

author = "Kolyada, \{V. I.\} and Lerner, \{A. K.\}",

year = "2005",

doi = "10.4064/sm171-1-1",

language = "אנגלית",

volume = "171",

pages = "1--13",

journal = "Studia Mathematica",

issn = "0039-3223",

publisher = "Institute of Mathematics, Polish Academy of Sciences",

number = "1",

}

TY - JOUR

T1 - On limiting embeddings of Besov spaces

AU - Kolyada, V. I.

AU - Lerner, A. K.

PY - 2005

Y1 - 2005

N2 - We investigate the classical embedding Bp,θs ⊂ Bq,θs-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.

AB - We investigate the classical embedding Bp,θs ⊂ Bq,θs-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.

KW - Besov space

KW - Embedding theorem

KW - Modulus of continuity

KW - Rearrangement estimate

UR - https://www.scopus.com/pages/publications/22944465468

U2 - 10.4064/sm171-1-1

DO - 10.4064/sm171-1-1

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:22944465468

SN - 0039-3223

VL - 171

SP - 1

EP - 13

JO - Studia Mathematica

JF - Studia Mathematica

IS - 1

ER -

On limiting embeddings of Besov spaces

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this