Hardy’s inequality in Musielak-Orlicz-Sobolev spaces. (English) Zbl 1316.46030

Maeda, Fumi-Yuki; Mizuta, Yoshihiro; Ohno, Takao; Shimomura, Tetsu

Hiroshima Math. J. 44, No. 2, 139-155 (2014).

Summary: Our aim in this paper is to treat Hardy’s inequalities for Musielak-Orlicz-Sobolev functions on proper open subsets of \(\mathbb {R}^N\).

MSC:

46E30	Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
46E35	Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
42B25	Maximal functions, Littlewood-Paley theory
26D10	Inequalities involving derivatives and differential and integral operators

Keywords:

Musielak-Orlicz space; Hardy’s inequality; variable exponent