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′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.
Sobolev embedding into BMO and weak-L ∞ for 1-dimensional probability measure.
FEO, Filomena;
2015-01-01
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′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.File in questo prodotto:
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