LAUSR

Some approximative characteristics of classes of periodic functions of many variables L β , p ψ , $$ {L}_{\beta, p}^{\psi }, $$ 1 < p < 1 , in a uniform metric are investigated. The first part of the paper is devoted to the construction of estimates of the best orthogonal trigonometric approximations of the mentioned classes in the space L∞ . In the second part, we have established the ordinal estimates of the orthoprojective widths of the classes L β , p ψ , $$ {L}_{\beta, p}^{\psi }, $$ 1 < p < 1 , in the same space, as well as the estimates of another approximative characteristic which is close, in a definite meaning, to the orthoprojective width.