GENERALIZED DIMENSION ESTIMATES FORIMAGES OF POROUS SETS IN METRIC SPACES

摘要

In Q-Ahlfors regular metric measure spaces we obtain essentially sharp dimension estimates for images of porous sets under Hajlasz-type Sobolev maps with L°-gradient. The esti- logt logt t Their method also yields generalized Hausdorff dimension estimates which were shown to be sharp for Hélder continuous maps.