Quasianalyticity and pluripolarity

Abstract

We show that the graph $${\Gamma }_f=\{(z,f(z))\in {\mathbb{C}}^2:z\in S\}$$ in ${\mathbb{C}}^2$ of a function $f$ on the unit circle $S$ which is either continuous and quasianalytic in the sense of Bernstein or $C^{\infty }$ and quasianalytic in the sense of Denjoy is pluripolar.