Mathematical Notes

, Volume 58, Issue 2, pp 824–832 | Cite as

Logarithmic growth of theL1-norm of the majorant of partial sums of an orthogonal series

  • B. S. Kashin
  • S. J. Szarek
Article

Abstract

It is proved that for anyN ×N orthogonal matrixA = {aij} we have
$$\sum\limits_{i = 1}^N {\mathop {\max }\limits_{1 \leqslant n \leqslant N} |\left| {\sum\limits_{j = 1}^n {a_{ij} } } \right|} \geqslant \frac{1}{{30}}N^{1/2} \log N.$$

A multidimensional analog of this result is also established.

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Copyright information

© Plenum Publishing Corporation 1996

Authors and Affiliations

  • B. S. Kashin
    • 1
  • S. J. Szarek
    • 2
  1. 1.Steklov Mathematical InstituteRussian Academy of SciencesMoscow
  2. 2.Case Western Reserve UniversityCleveland

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