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