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We obtain local estimates, also called propagation of smallness or Remez-type inequalities, for analytic functions in several variables. Using Carleman estimates, we obtain a three sphere-type inequality, where the outer two spheres can be any sets satisfying a boundary separation property, and the inner sphere can be any set of positive Lebesgue measure. We apply this local result to characterize the dominating sets for Bergman spaces on strongly pseudoconvex domains in terms of a density condition or a testing condition on the reproducing kernels. Our methods also yield a sufficient condition for arbitrary domains and lower-dimensional sets.
We prove some characterizations of Schatten class Toeplitz operators on Bergman spaces of tube domains over symmetric cones for small exponents.
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.
In this paper we introduce, via a Phragmen-Lindelof type theorem, a maximal plurisubharmonic function in a strongly pseudoconvex domain. We call such a function the {sl pluricomplex Poisson kernel} because it shares many properties with the classical
A radial weight $omega$ belongs to the class $widehat{mathcal{D}}$ if there exists $C=C(omega)ge 1$ such that $int_r^1 omega(s),dsle Cint_{frac{1+r}{2}}^1omega(s),ds$ for all $0le r<1$. Write $omegaincheck{mathcal{D}}$ if there exist constants $K=K(o
In this paper, we study the behavior of the weighted composition operators acting on Bergman spaces defined on strictly pseudoconvex domains via the sparse domination technique from harmonic analysis. As a byproduct, we also prove a weighted type est