English

Particle systems, Dipoles and Besov spaces of distributions

Analysis of PDEs 2025-11-27 v2 Functional Analysis

Abstract

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 H\"older spaces of functions with respect to an appropriately defined pseudo-metric.

Keywords

Cite

@article{arxiv.2411.14352,
  title  = {Particle systems, Dipoles and Besov spaces of distributions},
  author = {Mateus Marra and Pedro Morelli and Daniel Smania},
  journal= {arXiv preprint arXiv:2411.14352},
  year   = {2025}
}

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17 pages