Weighted inequalities for families of operators generated by truncated Ces\`aro kernels

K. S. Kazarian

Izvestiya. Mathematics , Tome 32 (1989) no. 2, pp. 289-311

Résumé

For subsystems of the trigonometric system of the form $\{e^{inx}\}_{|n|\geqslant k}$ and $\{e^{inx}\}_{\substack{|n|\geqslant k\\n\ne -k}}$ ($k=1,2,\dots$) this paper establishes necessary and sufficient conditions on a weight function $\psi$ for the given system to be a $(C,\alpha)$-basis ($\alpha>0$) in the space $L^p_{[-\pi,\pi]}(\psi)$, $1\leqslant p\infty$. Bibliography: 23 titles.