Approximation theorems in \(L^{p}\) spaces of functions
of several variables

Abstract. The direct and converse trigonometric approximation theorems in Lebesgue spaces of functions of several variables are proved by using moduli of smoothness of fractional order. Also, a constructive characterization of the generalized Lipschitz classes is obtained.

Key words and phrases. Best approximation, converse theorem, direct theorem, fractional modulus of smoothness, Lebesgue space.