On the Order of the Trigonometric Diameter of the Anisotropic Nikol’skii–Besov Class in the Metric of Anisotropic Lorentz Spaces

In this paper we estimate the order of the trigonometric diameters of the anisotropic Nikol’skii–Besov classes in the anisotropic Lorentz spaces. The order of the trigonometric diameter of the anisotropic Nikol’skii–Besov class B p r α τ ( T n ) is found in the metric of the anisotropic Lorentz spaces L q θ ( T n ) under the condition 1 < p = ( p 1 ,..., p n ) < 2 < q = ( q 1 ,..., q n ).