image-averaging domains and Poincaré inequalities with Orlicz norms Original Research Article

We characterize L(φ,μ)L(φ,μ)-averaging domains using the Whitney covers and the quasihyperbolic metric and study the invariance of L(φ,μ)L(φ,μ)-averaging domains under some mappings. As applications of the L(φ,μ)L(φ,μ)-averaging domains, we prove the Poincaré inequality with Orlicz norms for solutions of the non-homogeneous AA-harmonic equation in L(φ,μ)L(φ,μ)-averaging domains.