Compactness of Hankel operators with continuous symbols
  Let $\Omega$ be a bounded convex Reinhardt domain in $\mathbb{C}^2$ and $\phi\in C(\bar{\Omega})$. We show that the Hankel operator $H_{\phi}$ is compact if and only if $\phi$ is holomorphic along every non-trivial analytic disc in the boundary of $\Omega$. 
Timothy Clos and Sonmez Sahutoglu
math.CV math.FA