Sampling constants for dominating sets in generalized Fock spaces
Volume 275 / 2024
Studia Mathematica 275 (2024), 65-83
MSC: Primary 30H20; Secondary 30E99, 30D99
DOI: 10.4064/sm230514-7-2
Published online: 4 April 2024
Abstract
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.
