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We obtain order estimates of approximation of classes $B^{\Omega}_{p,\theta}$of periodic functions of many variables in the space $L_q$ by using operatorsof orthogonal projection as well as linear operators subjected to someconditions.

Estimates for approximation characteristics of the classes  $B^{\Omega}_{p,\theta}$ of periodic functions of many variables with a given  majorant of the mixed moduli of continuity