Dominating sets in Bergman spaces and sampling constants

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 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 conditio…

Sharp Bekolle estimates for the Bergman projection

We prove sharp estimates for the Bergman projection in weighted Bergman spaces in terms of the Bekolle constant. Our main tools are a dyadic model dominating the operator and an adaptation of a method of Cruz-Uribe, Martell and Perez.

广义Fock空间中的采样常数

Sampling constants in generalized Fock spaces

该研究证明了广义加倍Fock空间中支配集的Logvinenko-Sereda型定理，给出了采样常数对相对密度参数$γ$的精确多项式依赖，方法基于Remez型不等式和覆盖引理。

Wavelet frames, Bergman spaces and Fourier transforms of Laguerre functions

The Fourier transforms of Laguerre functions play the same canonical role in wavelet analysis as do the Hermite functions in Gabor analysis. We will use them as analyzing wavelets in a similar way the Hermite functions were recently by K. Groechenig and Y. Lyubarskii in "Gabor frames with Hermite functions, C. R. Acad. Sci. Paris, Ser. I 344 157-162 (2007)". Building on the work of K. Seip, "Beurling type density theorems in the unit disc, Invent. Math., 113, 21-39 (1993)", concerning sampling sequences on weighted Bergman spaces, we find a sufficient density condition for constructing frames …