PDEA Seminar: The Haar system in Besov and Triebel-Lizorkin spaces: survey of recent results
- Date: 3 June 2025, 10:15–11:00
- Location: Ångström Laboratory, 64119 + Zoom
- Type: Seminar
- Lecturer: Gustavo Garrigós (Universidad de Murcia)
- Organiser: Matematiska institutionen
- Contact person: Kaj Nyström
Gustavo Garrigós (Universidad de Murcia) gives this seminar. Welcome to join!
Abstract: We study the behavior of Haar coefficients in B and F-spaces on R, for an exotic parameter range in which the Haar system is not an unconditional basis. We present 3 results in this direction: First we show that, in the range 1/p< s < 1, the Besov norm continues to remain equivalent to the discrete Haar coefficient norm. Secondly, in the exotic region of parameters (s,p,q), we study the optimal inclusions between the B and F-classes and their dyadic counterparts, that is, the spaces of distributions whose Haar coefficients have a finite discrete b or f-norm. Finally, we present a new characterization of B and F-spaces in terms of the size of their doubly oversampled Haar coefficients, which is valid up to smoothness s<1.
This research is part of a joint work with A. Seeger and T. Ullrich.
Participate on site or via Zoom link, meeting ID: 67226102216. Ensure Zoom access by contacting the organisers in advance.
This is a seminar in the PDEs and Applications seminar series