Sampling constants for dominating sets in generalized Fock spaces

S Konate (1, 2) , Marcu-Antone Orsoni (2)

1 IUFP, Université de Ségou
2 IMB - Institut de Mathématiques de Bordeaux

We prove several results related to a Logvinenko–Sereda-type theorem on dominating sets for generalized doubling Fock spaces. In particular, we give a precise polynomial dependence of the sampling constant on the relative density parameter $\gamma$ of the dominating set. Our method is an adaptation of that used in [J. Math. Anal. Appl. 495 (2021), no. 2, art. 124755] for the Bergman spaces and is based on a Remez-type inequality and a covering lemma related to doubling measures.

Mots clés: Dominating sets; Sampling constant; Fock space; Reverse Carleson measure

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

S Konate, Marcu-Antone Orsoni. Sampling constants for dominating sets in generalized Fock spaces. Studia Mathematica, In press, ⟨10.4064/sm230514-7-2⟩. ⟨hal-03174991v4⟩