Estimations of the best M -term approximations of functions in the Lorentz space with constructive methods

Abstract

This paper considers the Lorentz space of periodic functions of many variables with the anisotropic norm, of functional Nikol’skii-Besov’s class and of the best M -term approximation of function. We have established sufficient conditions for the function to belong to one of the Lorentz spaces in another. We obtain upper and lower bounds for the best M -member approximations of functions from the Nikol’skii-Besov class in the anisotropic Lorentz space To prove the upper bound, we used a new constructive method developed by V.N. Temlyakov.