论文标题
汉克尔操作员的紧凑性，在凸域上具有连续符号
Compactness of Hankel operators with continuous symbols on convex domains
论文作者
论文摘要
令$ω$为$ \ mathbb {c}^{n} $，$ n \ geq 2 $，$ 1 \ leq q \ leq（n-1）$和$ ϕ \ in C（\barΩ）$中的有界凸域。如果hankel运算符$ h^{q-1} _D $（0，q-1）$ - 带有符号$ ϕ $的表单是紧凑的，那么$ ϕ $沿$ q $ - dimensional Analytic（实际上，offine offine）在边界中的品种。我们还证明了部分相反：如果边界仅包含“有限的多个”品种，$ 1 \ leq q \ leq n $，而c（\barΩ）$中的$ ϕ \ in c（\barΩ）$是沿尺寸$ q $（或更高）的分析性的，则是$ h^{q-1} _D = $ compact。
Let $Ω$ be a bounded convex domain in $\mathbb{C}^{n}$, $n\geq 2$, $1\leq q\leq (n-1)$, and $ϕ\in C(\barΩ)$. If the Hankel operator $H^{q-1}_ϕ$ on $(0,q-1)$--forms with symbol $ϕ$ is compact, then $ϕ$ is holomorphic along $q$--dimensional analytic (actually, affine) varieties in the boundary. We also prove a partial converse: if the boundary contains only `finitely many' varieties, $1\leq q\leq n$, and $ϕ\in C(\barΩ)$ is analytic along the ones of dimension $q$ (or higher), then $H^{q-1}_ϕ$ is compact.
