An Orlicz-Besov Poincaré Inequality via John Domains - Hongyan Sun (Journal of Function Spaces)
Denote by B˙⁎α,ϕ(Ω) the intrinsic Orlicz-Besov space, where α∈R, ϕ is a Young function, and Ω⊂Rn is a domain. For α∈(-n,0) and optimal ϕ, via John domains, we establish criteria for bounded domains Ω⊂Rn supporting an Orlicz-Besov Poincaré inequality. ‖u-uΩ‖Ln/|α|(Ω)≤C‖u‖B˙⁎α,ϕ(Ω)  ∀u∈B˙⁎α,ϕ(Ω). This extends the known criteria for bounded domains supporting Sobolev-Poincaré inequality and its fractional analogue.