Bergman空间中的Weissler和Bernoulli型不等式
Weissler and Bernoulli type inequalities in Bergman spaces
摘要：
考虑了具有一般径向权的Bergman空间的Weissler型不等式，给出了权$w$关于其矩的条件，使得当$n\in \mathbb{N}$和$0< r\le 1/\sqrt{n}$时，$\|f_r\|_{A^{2n}(w)}\leq \|f\|_{A^2(w)}$.对于非整数指数，证明了该不等式的一个特例，它可以看作是Bernoulli不等式的一种类似形式。构造了一个单调权重的例子，证明了这些不等式不再成立。
英文摘要：
We consider Weissler type inequalities for Bergman spaces with general radial weights and give conditions on the weight $w$ in terms of its moments ensuring that $\|f_r\|_{A^{2n}(w)}\leq \|f\|_{A^2(w)}$ whenever $n\in \mathbb{N}$ and $0< r\le 1/\sqrt{n}$. For noninteger exponents a special case of this inequality is proved which can be considered as a certain analog of the Bernoulli inequality. An example of a monotonic weight is constructed for which these inequalities are no longer true.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
