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Zeitschrift für Analysis und ihre Anwendungen


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Volume 16, Issue 3, 1997, pp. 669–687
DOI: 10.4171/ZAA/784

Published online: 1997-09-30

Marcinkiewicz-Zygmund-Type Inequalities Trigonometric Interpolation on Non-Uniform Grids and Unconditional Schauder Bases in Besov Spaces on the Torus

Konstantin V. Runovski[1] and Winfried Sickel[2]

(1) Lomonosov State University, Sevastopol, Ukraine
(2) Friedrich-Schiller-Universität Jena, Germany

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.

Keywords: Marcinkiewicz-Zygmund inequalities, trigonometric interpolation on non-uniform grids, rate of convergence in Besov spaces on the torus, unconditional Schauder bases in Besov spaces on the torus

Runovski Konstantin, Sickel Winfried: 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), 669-687. doi: 10.4171/ZAA/784