A CHARACTERIZATION OF ORLICZ-POINCARÉ INEQUALITY ON METRIC MEASURE SPACES

MARCELINA MOCANU

Department of Mathematics, Informatics and Education Sciences, Faculty of Sciences, "Vasile Alecsandri" University of Bacău, Calea Mărăşeşti 157, Bacău 600115, ROMANIA,
e-mail: mmocanu@ub.ro

Abstract

In this note we characterize a weak Orlicz-Poincaré inequality through the Hölder conti-nuity of locally integrable functions possessing upper gradients in the corresponding Or-licz space, under some growth assumptions on the Young function. Our results are proved in the setting of doubling metric measure spaces.

Keywords

Ahlfors regular metric measure space Poincaré inequality Orlicz-Sobolev space Hölder continuity quasiconvex curve modulus of a family of curves