Geodesic
On the Fourier--Walsh coefficients
Izvestiya. Mathematics , Tome 4 (1970) no. 1, pp. 209-214.

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We obtain sharp lower bounds on the Fourier–Walsh coefficients of a continuous function. 
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S. V. Bochkarev. On the Fourier--Walsh coefficients. Izvestiya. Mathematics , Tome 4 (1970) no. 1, pp. 209-214. http://geodesic.mathdoc.fr/item/IM2_1970_4_1_a10/

[1] Fine N. I., “On the Walsh functions”, Trans. Amer. Math. Soc., 65 (1949), 372–414 | DOI | MR | Zbl

[2] Kachmazh S., Shteingauz G., Teoriya ortogonalnykh ryadov, M. Gos. izd-vo fizmat literatury, 1958 | MR

[3] Zigmund A., Trigonometricheskie ryady, t. I, Mir, M., 1965 | MR