Marcinkiewicz-Zygmund-type inequalities for irregular knots and mixed metrics

Preprint series: 98-25, Analysis

The paper is published: Vestnik RUDN, Mathematik, 4,5 (1), 90-115, 1997/98

MSC:
42B05 Fourier series and coefficients
42B15 Multipliers

Abstract: Marcinkiewicz-Zygmund type inequalities on the equivalence of a continuous norm of a real-valued
trigonometric polynomial of $\; l \,$ variables and its discrete one are proved in the general case of mixed
$\; L_{\overline{p}}$-metrics, where $\; {\overline{p}} = (p_1,...,p_l);\;\; 0 < p_i \le +\infty, \;\; i=1,....,l,\,$ and
of non-uniform grids. A new representation formula for a trigonometric polynomial, which contains a parameter
is used to prove the main results.

Keywords: discrete and continuous quasi-norms