In this article, we characterize the classes Spw classes in terms of the boundary behavior of Berezin symbols of the weighted shift operators on the Dirichlet space DD. Also, we give a result related with the asymptotic multiplicative property of the Berezin symbol of any operator on reproducing kernel Hilbert space. Moreover, by using Berezin symbols, we give some condition for st-DL convergence of a series of complex numbers.