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MR1367220 42C15
Kashin, B. S.; Sharek, S. I. Logarithmic growth of the $L^1$-norm of the majorant of partial sums of an orthogonal series. (Russian) Mat. Zametki 58 (1995), no. 2, 218--230, 319; translation in Math. Notes 58 (1995), no. 1-2, 824–832 (1996)
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