2 papers
math.FA2024
Borel regularity is equivalent to Lusin's theorem and the existence of Borel representatives
Ryan Alvarado, PrzemysÅaw Górka, Artur SÅabuszewski
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.…
math.FA2024
Compact embeddings of Sobolev, Besov, and Triebel-Lizorkin spaces
Ryan Alvarado, PrzemysÅaw Górka, Artur SÅabuszewski
We establish necessary and sufficient conditions guaranteeing compactness of embeddings of fractional Sobolev spaces, Besov spaces, and Triebel-Lizorkin spaces, in the general cont…