Best multivariate approximations by trigonometric polynomials with frequencies from hyperbolic crosses (Q1375384)

The author proves two theorems presenting a characterization of smoothness properties which govern preassigned degrees of the approximations of multivariate periodic functions by trigonometric polynomials with the frequencies from so-called hyperbolic crosses in terms of new moduli of smoothness. The methods employed in the proofs are further developments of those in the proofs of quasinorm equivalence theorems for certain Hölder and Besov spaces of mixed smoothness.