Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 43, 2018, 1027-1043

A NEW CARTAN-TYPE PROPERTY AND STRICT QUASICOVERINGS WHEN p = 1 IN METRIC SPACES

Panu Lahti

University of Jyväskylä, Department of Mathematics and Statistics
P.O. Box 35, FI-40014 University of Jyväskylä, Finland; panu.k.lahti 'at' jyu.fi

Abstract. 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.

2010 Mathematics Subject Classification: Primary 30L99, 31E05, 26B30.

Key words: Metric measure space, function of bounded variation, fine topology, Cartan property, strict quasicovering, fine Newton–Sobolev space.

Reference to this article: P. Lahti: A new Cartan-type property and strict quasicoverings when p = 1 in metric spaces. Ann. Acad. Sci. Fenn. Math. 43 (2018), 1027-1043.

Full document as PDF file

https://doi.org/10.5186/aasfm.2018.4364