Order estimates of the modulus of variation of the sum of a lacunary trigonometric series

We find order estimates for the modulus of variation and the averaged modulus of the sum of a lacunary trigonometric series in terms of its coefficients. These interesting global characteristics of a function and their applications have been studied in papers by Chanturiya, Dolzhenko, Sevast'yanov, Sendov, Popov, and others. Since the sum of a lacunary trigonometric series has frequently been used in the theory of functions to provide an example of a function having one property or another, it is useful to know as much as possible about such a function, especially such global characteristics as the modulus of variation and the averaged modulus. We also give necessary and sufficient conditions for the sum of a lacunary trigonometric series to belong to certain classes of functions defined in terms of these characteristics.