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

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