Approximation of functions from \(L^p(\omega)_\beta\) by general linear operators (Q519992)

The paper under review is interested in pointwise convergence of \(A\)-transformations of Fourier series (or of its conjugate), where \(A=\big(a_{n,k}\big)\) is an infinite lower triangular matrix with non negative entries and normalized rows: \centerline{does \(T_Af(x)=\displaystyle\sum_{k=0}^n a_{n,k} S_k(f)(x)\longrightarrow f(x)\) ?}\smallskip (here \(S_k(f)\) stands for the \(k^{th}\) partial sum of the Fourier series) \medskip The paper contains a list of several theorems around this topic which are variants from one another, with hypothesis in terms of various weighted \(L^p\)-moduli of continuity.