Dominating sets in Bergman spaces and sampling constants

Andreas Hartmann (1) , Dantouma Kamissoko (2) , Konaté Siaka (1, 3, 4) , Marcu-Antone Orsoni (1)

1 IMB - Institut de Mathématiques de Bordeaux
2 Université de Ségou
3 Université de Ségou
4 USTTB - Université des Sciences, des Techniques et des Technologies de Bamako

We discuss sampling constants for dominating sets in Bergman spaces. Our method is based on a Remez-type inequality by Andrievskii and Ruscheweyh. We also comment on extensions of the method to other spaces such as Fock and Paley-Wiener spaces.

Mots clés: Dominating sets; reverse Carleson measure; Bergman space; sampling

Domaines: Variables complexes [math.CV]; Analyse classique [math.CA]

Andreas Hartmann, Dantouma Kamissoko, Konaté Siaka, Marcu-Antone Orsoni. Dominating sets in Bergman spaces and sampling constants. Journal of Mathematical Analysis and Applications, 2021, 495 (17), pp.124755. ⟨hal-02539923v2⟩