Hokkaido Mathematical Journal

Hardy's inequality in Orlicz-Sobolev spaces of variable exponent

Yoshihiro MIZUTA, Eiichi NAKAI, Takao OHNO, and Tetsu SHIMOMURA

Full-text: Open access

Abstract

Our aim in this paper is to deal with a norm version of Hardy's inequality for Orlicz-Sobolev functions with $|\nabla u| \in L^{p(\cdot)}\log L^{p(\cdot)q(\cdot)}(\Omega)$ for an open set $\Omega \subset \R^n$. Here $p(\cdot)$ and $q(\cdot)$ are variable exponents satisfying log-H\"older and loglog-H\"older conditions, respectively. We are also concerned with the case when $p$ attains the value 1 in some parts of the domain is included in the results.

Article information

Source
Hokkaido Math. J., Volume 40, Number 2 (2011), 187-203.

Dates
First available in Project Euclid: 7 July 2011

Permanent link to this document
https://projecteuclid.org/euclid.hokmj/1310042827

Digital Object Identifier
doi:10.14492/hokmj/1310042827

Mathematical Reviews number (MathSciNet)
MR2840104

Zentralblatt MATH identifier
1227.46023

Subjects
Primary: 46E30: Spaces of measurable functions (Lp-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) 42B25: Maximal functions, Littlewood-Paley theory

Keywords
variable exponent Lebesgue space Hardy's inequality Sobolev embeddings

Citation

MIZUTA, Yoshihiro; NAKAI, Eiichi; OHNO, Takao; SHIMOMURA, Tetsu. Hardy's inequality in Orlicz-Sobolev spaces of variable exponent. Hokkaido Math. J. 40 (2011), no. 2, 187--203. doi:10.14492/hokmj/1310042827. https://projecteuclid.org/euclid.hokmj/1310042827


Export citation