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We obtain the exact order of deviations of Fejér sums on the class of continuous functions. This order is determined by a given majorant of the best approximations.In the present paper, we establish the order of decrease of the least upper bound of deviations of Fejér sums on the classes of 2π-periodic functions of many variables determined by restrictions imposed on the sequence of the best approximations. In particular, we generalize a one-dimensional result of Stechkin to the case of functions of many variables.Consider the space C T d

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In this paper, the structural properties of a function are characterized by moduli of continuity. The classical Hardy-Littlewood theorem describes a relation between the smoothness of the analytic function boundary values at the boundary of its analyticity and the growth rate of the modulus of its higher-order derivatives. An analogue of the Hardy-Littlewood theorem has been obtained for functions from the class Hp and higher-order moduli of continuity.