Article ID Journal Published Year Pages File Type
6418095 Journal of Mathematical Analysis and Applications 2015 18 Pages PDF
Abstract

We characterize rearrangement invariant spaces X with respect to a suitable 1-dimensional probability μ (e.g. log-concave measure) such that the Sobolev embedding‖u‖BMO(R,μ)≤C(‖u′‖X+‖u‖L1(R,μ)) holds for any function u∈L1(R,μ), whose real-valued weakly derivative u′ belongs to X. Here BMO(R,μ) is the space of functions with bounded mean oscillation with respect to μ. We investigate the embedding in weak-L∞(R,μ), too.

Related Topics
Physical Sciences and Engineering Mathematics Analysis
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