Dominating Sets in Bergman Spaces on Strongly Pseudoconvex Domains

We obtain local estimates, also called propagation of smallness or Remez-type inequalities, for analytic functions in several variables. Using Carleman we a three sphere-type inequality, where the outer two spheres can be any sets satisfying boundary separation property, and inner sphere set positive Lebesgue measure. apply this result to characterize dominating Bergman spaces on strongly pseudoconvex domains terms density condition testing reproducing kernels. Our methods yield sufficient arbitrary lower-dimensional sets.