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.
