Best Approximation of the Conjugate Functions in Morrey Spaces

Abstract

We investigate the best approximation of the conjugate functions in Morrey spaces. The best approximation of the conjugate functions have been obtained in terms of the best approximation of the functions. Some direct and inverse theorems for approximation by trigonometric polynomials in Morrey spaces are proved. The modulus of smoothness of conjugate functions were estimated in terms of the best approximation of the given functions.