$\mathbb C^2$中凸Reinhardt域的Leray变换的谱
The spectrum of the Leray transform for convex Reinhardt domains in $\mathbb C^2$
摘要：
研究了$\mathbb C^2$中一类凸Reinhardt域的Leray变换及其边界算子.我们的阶级是自对偶的;它包含了一些边界小于$C^2$ -光滑的区域和一些边界光滑且退化Levi型的区域。证明了$L^2$ -正则性，并计算了包含曲面测度的一类边界测度的本质谱。一个对偶原理的建立提供明确的酉等价的域上的运营商在我们的类和相应的极域上的运营商。其中许多结果是新的，即使是经典的光滑有界强凸Reinhardt域的情况下。
英文摘要：
The Leray transform and related boundary operators are studied for a class of convex Reinhardt domains in $\mathbb C^2$. Our class is self-dual; it contains some domains with less than $C^2$-smooth boundary and also some domains with smooth boundary and degenerate Levi form. $L^2$-regularity is proved, and essential spectra are computed with respect to a family of boundary measures which includes surface measure. A duality principle is established providing explicit unitary equivalence between operators on domains in our class and operators on the corresponding polar domains. Many of these results are new even for the classical case of smoothly bounded strongly convex Reinhardt domains.
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