A new Cartan-type property and strict quasicoverings when P = 1 in metric spaces
Lahti, P. (2018). A new Cartan-type property and strict quasicoverings when P = 1 in metric spaces. Annales Academiae Scientiarum Fennicae Mathematica, 43, 1027-1043. doi:10.5186/AASFM.2018.4364
Published inAnnales Academiae Scientiarum Fennicae Mathematica
© The Author & Academia Scientiarum Fennica, 2018.
In a complete metric space that is equipped with a doubling measure and supports a Poincaré inequality, we prove a new Cartan-type property for the fine topology in the case p = 1. Then we use this property to prove the existence of 1-finely open strict subsets and strict quasicoverings of 1-finely open sets. As an application, we study fine Newton–Sobolev spaces in the case p = 1, that is, Newton–Sobolev spaces defined on 1-finely open sets.