2024/11/21 by Mateus Marra, Marra, Mateus, Pedro Morelli +3
Mathematics · Physics and Astronomy · #43A15 #43A85 #46E36 #46F99 #Analysis of PDEs (math.AP) #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #FOS: Mathematics #Functional Analysis (math.FA) #Gas Dynamics and Kinetic Theory
paper · pdf · doi:10.48550/arxiv.2411.14352
openalex publication_date 2024/11/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We define distributions on an abstract measure space endowed with a sequence of partitions, and introduce analogues of Besov spaces with negative smoothness in this setting. In particular, we describe these spaces of distributions using unconditional Schauder bases consisting either of Haar wavelets or of pairs of Dirac masses (dipoles). This framework allows us to obtain duality results between Besov spaces of negative smoothness and Hölder spaces of functions with respect to an appropriately defined pseudo-metric.