The embedding and approximation of classes of functions with a dominant mixed difference

We obtain a criterion for embedding the class $SH_p^\Omega$ into that $SB_{q,\theta}^{\Omega^*}$ ($1<p\leq q<\infty$). We also determine the exact order of the best approximations of functions from classes $SB_{p,\theta}^\Omega$ by trigonometric polynomials whose harmonics belong to sets generated by level surfaces of the majorant $\Lambda(t)$.