Poincaré-type inequalities with Lp(logL)αLp(logL)α-norms for Green’s operator

In this paper, we first establish local Poincaré-type inequalities with Lp(logL)αLp(logL)α-norms for Green’s operator applied to the solutions of the nonhomogeneous A-harmonic equation. Then, we extend the local results to global versions in the Lφ(μ)Lφ(μ)- domain.