标题： 凸泛函在加权 Bergman 空间上的稳定性及其应用 显示英文标题

标题： Stability of convex functionals on weighted Bergman spaces with applications

摘要： 最近，库利科夫（\cite{Ku}）证明了加权Bergman空间上的某些凸泛函被再生核最大化。 我们证明了当函数接近再生核时，这些泛函具有接近最大值。 这是在定量意义上证明的，其中范数和指数都是最优的，常数是显式的。 我们给出了一些应用和相关例子。 显示英文摘要

摘要： Recently, Kulikov (\cite{Ku}) has shown that certain convex functionals on weighted Bergman spaces are maximized by reproducing kernels. We prove that the same functionals hves near-maximal values for functions that are close to reproducing kernels. This is proved in a quantitative sense where both the norm and the exponent are optimal and the constant is explicit. We give several applications and some relevant examples.