Wiener's positive Fourier coefficients theorem in variants of \(L^p\) spaces
The authors consider the following classes of functions: the space \(L^p({\mathbb T)}\); the class of functions \(f\) with nonnegative Fourier coefficients such that \(|f|^p\) is integrable in a neighbourhood of \(0\); the space of functions whose Fourier coefficients belong to \(\ell^{p'}\); the space of functions \(f\) whose Fourier coefficients \(\{c_n\}\) satisfy \(\sum|c_n|\cdot|n|^{p-2}<\infty\); and the mixed norm spaces \(\ell^{p',2}\), \(1<p<2\). Various relationships between these classes are described.
scientific article; zbMATH DE number 5723343