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?Rn is a domain. For α∈(-n,0) and optimal ?, 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,?(Ω)???u∈B˙?α,?(Ω). This extends the known criteria for bounded domains supporting Sobolev-Poincaré inequality and its fractional analogue.