Approximation by Trigonometric Polynomials in Rearrangement Invariant Quasi Banach Function Spaces

Abstract

We investigate the approximation properties of trigonometric polynomials in rearrangement invariant quasi Banach function spaces. Relations between moduli of smoothness of the derivatives of a functions and those of the functions itself are studied. We prove a theorem on the relationship between the modulus of smoothness and the best approximation in rearrangement invariant quasi Banach function spaces. © 2014, Springer Basel.