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:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11367/43610
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 1
  • ???jsp.display-item.citation.isi??? 1
social impact