Geodesic
Logarithmic growth of the $L^1$-norm of the majorant of partial sums of an orthogonal series
Matematičeskie zametki, Tome 58 (1995) no. 2, pp. 218-230 
B. S. Kashin; S. I. Sharek. Logarithmic growth of the $L^1$-norm of the majorant of partial sums of an orthogonal series. Matematičeskie zametki, Tome 58 (1995) no. 2, pp. 218-230. http://geodesic.mathdoc.fr/item/MZM_1995_58_2_a4/
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     title = {Logarithmic growth of the $L^1$-norm of the majorant of partial sums of an orthogonal series},
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Voir la notice de l'article provenant de la source Math-Net.Ru

It is proved that for any $N\times N$ orthogonal matrix $A=\{a_{ij}\}$ we have $$ \sum_{i=1}^N\max_{1\le n\le N}\biggl|\sum_{j=1}^na_{ij}\biggr| \ge\frac 1{30}N^{1/2}\log N. $$ A multidimensional analog of this result is also established.

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