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Zbl 1166.46308
Tuominen, Heli
Characterization of Orlicz--Sobolev space. (English)
[J] Ark. Mat. 45, No. 1, 123-139 (2007). ISSN 0004-2080; ISSN 1871-2487/e

Summary: We give a new characterization of the Orlicz--Sobolev space $W ^{1,\Psi}(\bbfR^n)$ in terms of a pointwise inequality connected to the Young function $\Psi$. We also study different Poincaré inequalities in the metric measure space.

MSC 2000:: *46E35 Sobolev spaces and generalizations
46E30 Spaces of measurable functions
26D10 Inequalities involving derivatives, diff. and integral operators

Keywords: Orlicz-Sobolev space; Poincaré inequalities; metric measure space

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Zentralblatt MATH Berlin [Germany]