For a measure mu on R-n (or on a doubling metric measure space) and a Young function phi, we define two versions of Orlicz-Poincare inequalities as generalizations of the usual p-Poincare inequality. It is shown that, on R, one of them is equivalent to the boundedness of the Hardy-Littlewood maximal operator from L-phi(R, mu to L-phi R, mu.), while the other is equivalent to a. generalization of the Muckerthoupt A(p)-condition. While one direction in these equivalences is valid only on R, the other holds in the general setting of doubling metric measure spaces. We also characterize both Orlicz-Poincare inequalities oil metric measure spaces by means of pointwise inequalities involving maximal functions of the gradient.
2010. Vol. 140, 31-48 p.