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Fourier coefficients of characteristic functions of intervals with respect to a complete orthonormal system bounded in $$L^p([0,1])$$, $$2<p<\infty$$. (English. Russian original) Zbl 1322.42034
Math. Notes 97, No. 4, 647-651 (2015); translation from Mat. Zametki 97, No. 4, 632-635 (2015).
Main result: for any orthonormal system $$\{\phi_j\}_{j=1}^{\infty}$$ which is complete in $$L^2([0,1])$$ and uniformly bounded in $$L^p([0,1]),2<p<\infty,$$ there exists $$x\in (0,1]$$ such that $\sum_{j=1}^{\infty}\left|\int_0^x\phi_j(t)dt\right|^{(p-2)/(p-1)}=\infty.$
##### MSC:
 42C10 Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.)
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##### References:
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