Characterization of Besov spaces associated with parabolic sections
The authors prove some topological properties of Besov spaces associated with a family of parabolic sections described by monotonic increasing functions. Such functional structure is known to be closely related to the study of the parabolic Monge-Ampère equation. The main results are contained in Theorems~1.5, 1.8 and~1.11. At first the authors prove a duality pairing between Besov spaces by using an approximation of the identity. Then, some duality results for Besov spaces are proved using only the doubling property. The third main result of this paper concerns a continuous embedding between Besov spaces which they prove coupling the doubling property with a lower bound condition. Given these Besov spaces associated with the introduced family of parabolic sections, many problems and challenges can be raised such as the regularity of solutions to the parabolic Monge-Ampère equation with initial data in Besov spaces. I think that this paper will be of great interest.
scientific article; zbMATH DE number 7317193
scientific article