Equivalent quasi-norms involving differences and moduli of continuity in anisotropic Nikol’skii–Besov spaces

In this paper we study the equivalence of quasi-norms in the anisotropic Nikol’skii–Besov $B_{p,\theta}^l(\mathbb{R}^n)$ spaces involving differences and moduli of continuity for $0<p, \theta\leqslant\infty$.