Title: Optimality of Orlicz Domain in Sobolev Embeddings
Speaker: Vit Musil (Charles University)
Abstract: Given a rearrangement-invariant Banach function space $Y(\Omega)$, we consider the problem of the existence of an optimal (largest) domain Orlicz space $L^A(\Omega)$ satisfying the Sobolev embedding $W^mL^A(\Omega) \hookrightarrow Y(\Omega)$. We present a solution of this problem within the class of Marcinkiewicz endpoint spaces which covers several important examples. It turns out that the answer is negative for these examples and it suggests that this tool is rather strong in negative cases. We also prove a certain sufficient condition for a positive result with no restriction to target spaces.
Seminar URL: https://research.math.osu.edu/aot/