  A space of analytic functions in the unit disc with uniformly continuous
derivatives is said to be quasianalytic if the boundary value of a non-zero
function from the class can not have a zero of infinite multiplicity. Such
classes were described in the 1950-s and 1960-s by Carleson, Rodrigues-Salinas
and Korenblum. A non-zero function from a quasianalytic space of analytic
functions can only have a finite number of zeros in the closed disc. Recently,
Borichev, Frank, and Volberg proved an explicit estimate on the number of
zeros, for the case of quasianalytic Gevrey classes. Here, an estimate of
similar form for general analytic quasianalytic classes is proved using a
reduction to the classical quasianalyticity problem.
