On the trigonometric approximation of functions in a weighted Lipschitz class (Q2026956)

The author considered functions from weighted Lipschitz classes \(W\left( L^{r},w\right) \) and their conjugate ones. He proved two theorems on approximations of such functions by the \(C^{1}T\) means of its Fourier series with respect to the weighted norm. The function \( w\) was used as a measure of such approximations. The author used interesting assumptions on the function \(w,\) thanks to which it was possible to obtain the best orders of approximation. Some corollaries with generalization and improvement of various results available in the literature, for special functions \(w\) and selected matrix methods, were derived.