GEHRING'S LEMMA FOR ORLICZ FUNCTIONS IN METRIC MEASURE SPACES AND HIGHER INTEGRABILITY FOR CONVEX INTEGRAL FUNCTIONALS

摘要

For the metric measure space (X, d, mu ) with a metric d and a Borel regular measure mu satisfying the doubling condition, we derive Gehring's lemma in the Orlicz setting by proving boundedness of Hardy-Littlewood maximal functions in X. As an application, the higher integrability of minimizers for the convex integral functional