On estimates of the order of the best M–term approximations of functions of several variables in the anisotropic Lorentz – Zygmund space

Abstract

The article considers the anisotropic  Lorentz – Karamata space of periodic functions of several variables and the Nikol'skii – Besov class in this space. The order-sharp estimates are established for the best $M$-term trigonometric approximations of functions from the Nikol'skii-Besov class in the norm of another Lorentz – Zygmund space.

Keywords

• lorentz – zygmund space
• nikol'skii – besov class
• m-term approximation