We investigate extensions of the classical Marcinkiewicz-Zygmund inequality to non-uniform grids. Then we show how this inequality can be used to characterize Besov spaces on the torus by means of approximation by corresponding interpolatory polynomials. One of these characterizations can be applied to the construction of unconditional Schauder bases.
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Konstantin V. Runovski, Winfried Sickel, Marcinkiewicz-Zygmund-Type Inequalities Trigonometric Interpolation on Non-Uniform Grids and Unconditional Schauder Bases in Besov Spaces on the Torus. Z. Anal. Anwend. 16 (1997), no. 3, pp. 669–687DOI 10.4171/ZAA/784