Convex domains, Hankel operators, and maximal estimates
Convex domains, Hankel operators, and maximal estimates
复制标题
凸域、汉克尔算子和最大估计
DOI：
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发表时间：
2019
影响因子：
1
通讯作者：
E. Straube
中科院分区：
文献类型：
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作者：
Mehmet Çelik;Sonmez Sahutoglu;E. Straube
设$1leq qleq (n-1)$。首先证明了凸域上$(0,q-1)$-形式上的Hankel算子是紧的必要条件是其符号沿边界上$q维解析变元是全纯的。因为极大估计（等价地，边界的Levi形式上的一个可比较的特征值条件）被证明有利于Hankel算子的紧性，这个结果意味着在凸域上，极大估计排除了边界上的解析变数，除了顶维$(n-1)$（及其子变数）。我们的一些技术应用于一般伪凸域，证明了如果列维形式具有可比较的特征值，或者等价地，如果该域允许极大估计，则紧性和亚椭圆性在某一层次上成立，当且仅当它们在所有层次上成立。
Let $1leq qleq (n-1)$. We first show that a necessary condition for a Hankel operator on $(0,q-1)$-forms on a convex domain to be compact is that its symbol is holomorphic along $q$-dimensional analytic varieties in the boundary. Because maximal estimates (equivalently, a comparable eigenvalues condition on the Levi form of the boundary) turn out to be favorable for compactness of Hankel operators, this result then implies that on a convex domain, maximal estimates exclude analytic varieties from the boundary, except ones of top dimension $(n-1)$ (and their subvarieties). Some of our techniques apply to general pseudoconvex domains to show that if the Levi form has comparable eigenvalues, or equivalently, if the domain admits maximal estimates, then compactness and subellipticity hold for forms at some level $q$ if and only if they hold at all levels.