**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*

**Upload:** 1998-12-01

**Update:** 1999-01-29

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