𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Spaces of Bessel-potential type and embeddings: the super-limiting case

✍ Scribed by Júlio S. Neves

Publisher
John Wiley and Sons
Year
2004
Tongue
English
Weight
273 KB
Volume
265
Category
Article
ISSN
0025-584X

No coin nor oath required. For personal study only.

✦ Synopsis

Abstract

We consider Bessel‐potential spaces modelled upon Lorentz‐Karamata spaces and establish embedding theorems in the super‐limiting case. In addition, we refine a result due to Triebel, in the context of Bessel‐potential spaces, itself an improvement of the Brézis‐Wainger result (super‐limiting case) about the “almost Lipschitz continuity” of elements of H^1+n/p^~p~ (ℝ^n^). These results improve and extend results due to Edmunds, Gurka and Opic in the context of logarithmic Bessel potential spaces. We also give examples of embeddings of Besselpotential type spaces which are not of logarithmic type. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

📜 SIMILAR VOLUMES

Sharpness and non-compactness of embeddi
Sharpness and non-compactness of embeddings of Bessel-potential-type spaces
✍ Amiran Gogatishvili; Júlio Severino Neves; Bohumír Opic 📂 Article 📅 2007 🏛 John Wiley and Sons 🌐 English ⚖ 182 KB

## Abstract We establish embeddings for Bessel potential spaces modeled upon Lorentz–Karamata spaces with order of smoothness less than one. The target spaces are of Hölder‐continuous type. In the super‐limiting case we also prove that the embedding is sharp and fails to be compact. (© 2007 WILEY‐V

On the Bourgain, Brezis, and Mironescu T
On the Bourgain, Brezis, and Mironescu Theorem Concerning Limiting Embeddings of Fractional Sobolev Spaces
✍ V. Maz'ya; T. Shaposhnikova 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 112 KB

The article is concerned with the Bourgain, Brezis and Mironescu theorem on the asymptotic behaviour of the norm of the Sobolev-type embedding operator: W s;p ! L pn=ðnÀspÞ as s " 1 and s " n=p: Their result is extended to all values of s 2 ð0; 1Þ and is supplied with an elementary proof. The relati

Regularity of convolution type operators
Regularity of convolution type operators with PC symbols in Bessel potential spaces over two finite intervals
✍ L. P. Castro 📂 Article 📅 2003 🏛 John Wiley and Sons 🌐 English ⚖ 196 KB

## Abstract Convolution type operators acting between Bessel potential spaces defined on a union of two finite intervals are studied from the point of view of their regularity properties. The operators are assumed to have kernels with Fourier transforms in the class of piecewise continuous matrix f