Best m-term trigonometric approximations of the isotropic Nikol'skii-Besov-type classes of periodic functions of several variables

Keywords:
periodic function of several variables, Nikol'skii-Besov-type class, best m-term trigonometric approximationAbstract
We obtained the exact order estimates of the best m-term trigonometric approximations of the isotropic Nikol'skii-Besov-type classes Bωp,θ of periodic functions of several variables in the spaces Bq,1 for 1<p<q<∞, q≥2. A peculiarity of these spaces, as linear subspaces of Lq, is that the norm in them is stronger than the Lq-norm. It was found that the obtained estimates of the considered approximation characteristic coincide in order with the estimates of the corresponding characteristic of the classes Bωp,θ in the spaces Lq.