Order Equalities in Different Metrics for Moduli of Smoothness of Various Orders

In this paper, we obtain order equalities for the kth order Lq(T)-moduli of smoothness ωk(f;δ)q in terms of expressions that contain the lth order Lp(T)-moduli of smoothness ωl(f;δ)p on the class of periodic functions f∈Lp(T) with monotonically decreasing Fourier coefficients, where 1<p<q<∞, k,l∈N, and T=(−π,π]