Lebesgue Constants and Approximation of Classes of Functions with Bounded Derivative by Polynomials

Abstract

The norms of multiplier operators are called the Lebesgue constants. In the case of the space C(𝕋m) (or L(𝕋m)) the Lebesgue constants are represented by the integrals $$ {(2\pi )^{ - m}}\int\limits_{{T^m}} {\left| {\sum\limits_k {{\lambda _{n,k}}{e^{i(k,x)}}} } \right|dx} $$ .