An Orlicz-Besov Poincaré Inequality via John Domains

摘要

Denote by B_*~( α,?) (Ω) the intrinsic Orlicz-Besov space,where α ∈ R, ? is a Young function, and Ω ? R~n is a domain. For α ∈ (?n,0) and optimal ?, via John domains, we establish criteria for bounded domains Ω ? R~n supporting an Orlicz-Besov Poincaré inequality. ‖u ? u_Ω‖_(L~(n/|α|)_((Ω)) ≤ C‖u‖B_? (α,?) (Ω) ?u ∈ B_*~( α,?) (Ω). This extends the known criteria for bounded domains supporting Sobolev-Poincaré inequality and its fractional analogue.