✦ LIBER ✦

Sobolev embeddings for Riesz potential space of variable exponent

✍ Scribed by Toshihide Futamura; Yoshihiro Mizuta; Tetsu Shimomura

Publisher: John Wiley and Sons
Year: 2006
Tongue: English
Weight: 152 KB
Volume: 279
Category: Article
ISSN: 0025-584X
DOI: 10.1002/mana.200410432

No coin nor oath required. For personal study only.

✦ Synopsis

Abstract

📜 SIMILAR VOLUMES

Riesz potential and Sobolev embeddings o

Riesz potential and Sobolev embeddings on generalized Lebesgue and Sobolev spaces Lp(·) and Wk,p(·)

✍ Lars Diening 📂 Article 📅 2004 🏛 John Wiley and Sons 🌐 English ⚖ 210 KB

## Abstract We study the Riesz potentials __I~α~f__ on the generalized Lebesgue spaces __L__^__p__(·)^(ℝ^__d__^), where 0 < __α__ < __d__ and __I~α~f__(__x__) ≔ ∫ |__f__(__y__)| |__x__ – __y__|^__α__ – __d__^ __dy__. Under the assumptions that __p__ locally satisfies |__p__(__x__) – __p__(__x__)| ≤

Sobolev's inequality for Riesz potential

Sobolev's inequality for Riesz potentials of functions in Morrey spaces of integral form

✍ Yoshihiro Mizuta; Tetsu Shimomura 📂 Article 📅 2010 🏛 John Wiley and Sons 🌐 English ⚖ 149 KB

Integrability of maximal functions for g

Integrability of maximal functions for generalized Lebesgue spaces with variable exponent

✍ Yoshihiro Mizuta; Takao Ohno; Tetsu Shimomura 📂 Article 📅 2008 🏛 John Wiley and Sons 🌐 English ⚖ 131 KB

## Abstract Our aim in this paper is to deal with integrability of maximal functions for generalized Lebesgue spaces with variable exponent. Our exponent approaches 1 on some part of the domain, and hence the integrability depends on the shape of that part and the speed of the exponent approaching