Estimates for the Best M–Term Approximations of Function Classes with Bounded Mixed Derivatives in Lorentz Spaces

Order-sharp estimates are eatablished for the best M-term approximations of functions from W r q,τ1 with respect to the multiple trigonometric system in the metric of Lp,τ2 for a number of relations between the parameters p, q, τ1, and τ2. Constructive methods of nonlinear approximation are used in the proofs of upper estimates in most of the main results.