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

On the number of zeros of functions in analytic quasianalytic classes