8 papers
Embeddings of variable Sobolev, Besov, and Triebel-Lizorkin spaces on metric measure spaces
Ryan Alvarado, Michał Dymek, Przemysław Górka +1
Sobolev-type embeddings on metric measure spaces encode a subtle interaction between the analytic regularity of functions and the geometry of the underlying domain space. In this p…
Borel regularity is equivalent to Lusin's theorem and the existence of Borel representatives
Ryan Alvarado, Przemysław Górka, Artur Słabuszewski
In this article, we characterize both Lusin's theorem and the existence of Borel representatives via the regularity properties of the measure in general topological measure spaces.…
New Characterizations of First Order Sobolev Spaces
Przemysław Górka, Kacper Kurowski
We provide new characterizations of Sobolev spaces that are true under some mild conditions. We study modified first order Sobolev spaces on metric measure spaces: -Ne…
Compact embeddings of Sobolev, Besov, and Triebel-Lizorkin spaces
Ryan Alvarado, Przemysław Górka, Artur Słabuszewski
We establish necessary and sufficient conditions guaranteeing compactness of embeddings of fractional Sobolev spaces, Besov spaces, and Triebel-Lizorkin spaces, in the general cont…
Chessboard and level sets of continuous functions
Michał Dybowski, Przemysław Górka
We provide the following result and its discrete equivalent: Let be a continuous function. Then, there exist a point an…
Maximal δ-separated sets in separable metric spaces and weak forms of choice
Michał Dybowski, Przemyslaw Górka, Paul Howard
We show that the statement ``In every separable pseudometric space there is a maximal non-strictly δ-separated set.'' implies the axiom of choice for countable families of sets. Th…