Abstract:
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 $L^p_{[-\pi,\pi]}(\psi)$, $1\leqslant p<\infty$.
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