ON ESTIMATION OF FOURIER AND QUASI-MONOTONE-FOURIER COEFFICIENTS OF FUNCTIONS IN NIKOL’SKII CLASSES - Rexhepi, Shpetim; Kera, Samet; Snopce, Halil (Matematichki Bilten, 2019)
An equivalent form of Nikol’skii class \(H(p,k,φ)\), \(p [1,∞]\), using a supplementary condition for function \(φ\) and best approximation is given. The estimation of Fourier coefficients of functions belonging to the class \(H(p,k,φ)\), \(p [1,∞]\), by means of best approximation and modulus of smoothness without giving supplementary conditions to the \(φ\) function is investigated. We discuss the problem for the functions with quasi-monotone Fourier coefficients as well.