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.
MetadataShow full item record
Showing items with similar title or keywords.
Existence and almost uniqueness for p-harmonic Green functions on bounded domains in metric spaces Björn, Anders; Björn, Jana; Lehrbäck, Juha (Elsevier, 2020)We study (p-harmonic) singular functions, defined by means of upper gradients, in bounded domains in metric measure spaces. It is shown that singular functions exist if and only if the complement of the domain has positive ...
Arroyo, Ángel; Llorente, José G. (American Mathematical Society, 2019)A metric measure space (X, d, t) is said to satisfy the strong annular decay condition if there is a constant C > 0 such that for each x E X and all 0 < r < R. If do., is the distance induced by the co -norm in RN, we ...
Rajala, Kai; Rasimus, Martti; Romney, Matthew (Springer, 2021)We consider extensions of quasiconformal maps and the uniformization theorem to the setting of metric spaces X homeomorphic to R2R2. Given a measure μμ on such a space, we introduce μμ-quasiconformal maps f:X→R2f:X→R2, ...
Eriksson-Bique, Sylvester; Vähäkangas, Antti V. (American Mathematical Society, 2019)We prove the self-improvement of a pointwise p-Hardy inequality. The proof relies on maximal function techniques and a characterization of the inequality by curves.
Schultz, Timo (Springer Berlin Heidelberg, 2018)We introduce a more restrictive version of the strict CD(K,∞) -condition, the so-called very strict CD(K,∞) -condition, and show the existence of optimal maps in very strict CD(K,∞) -spaces despite the possible ...