This article is cited in 2 papers

Logarithmic growth of the $L^1$-norm of the majorant of partial sums of an orthogonal series

B. S. Kashin^a, S. I. Sharek<sup>b

a</sup> Steklov Mathematical Institute, Russian Academy of Sciences
^b Case Western Reserve University

Abstract: 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.

Received: 27.01.1995

 English version: Mathematical Notes, 1995, 58:2, 824–832

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