Oscillation functionals in rearrangement-invariant spaces yield subcritical, supercritical, and critical embeddings, with critical regimes producing logarithmic Hansson-type refinements via a deviation function of ψ/ϕ_X that recover and extend classical endpoint results including Trudinger-type ones
Kub´ ıcek, Optimal function spaces and Sobolev embeddings (English summary), Studia Math.286(2026), no
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Oscillation Functionals and Embeddings in Rearrangement-Invariant Spaces
Oscillation functionals in rearrangement-invariant spaces yield subcritical, supercritical, and critical embeddings, with critical regimes producing logarithmic Hansson-type refinements via a deviation function of ψ/ϕ_X that recover and extend classical endpoint results including Trudinger-type ones