An imbedding result for generalized Orlicz - Sobolev spaces

Preprint series: 97-10, Analysis

The paper is published: Rev. Roumaine. Math. Pures Appl., 42 (no. 7-8), 555-565, 1997

MSC:
46E35 Sobolev spaces and other spaces of smooth'' functions, embedding theorems, trace theorems
46E30 Spaces of measurable functions ($L^p$-spaces, Orlicz spaces, Kothe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)

Abstract: Let $L_{\rho}(\Omega )$ be a rearrangement invariant Banach function space which contains an Orlicz space $L_{B}(\Omega )$. The aim of the paper is the obtaining of an embedding theorem for the abstract Sobolev space $W^1L_{\rho}(\Omega ).$

Keywords: generalized Orlicz - Sobolev space, rearrangement invariant Banach function space, Orlicz space