谱扰动理论与双权问题
Spectral perturbation theory and the two weights problem
摘要：
著名的两个权重问题在于刻画所有可能的权重对，使得Hardy投影在相应的加权$L^2$空间之间有界。1980年的Koosis定理给出了一种构造一类权对的方法。我们表明，Koosis定理是密切相关的（事实上，是一个直接的后果）的光谱扰动模型提出的德Branges在1962年。此外，我们表明，德Branges的模型提供了一个运营商的价值版本的Koosis定理。
英文摘要：
The famous two weights problem consists in characterising all possible pairs of weights such that the Hardy projection is bounded between the corresponding weighted $L^2$ spaces. Koosis' theorem of 1980 gives a way to construct a certain class of pairs of weights. We show that Koosis' theorem is closely related to (in fact, is a direct consequence of) a spectral perturbation model suggested by de Branges in 1962. Further, we show that de Branges' model provides an operator-valued version of Koosis' theorem.
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