Marcinkiewicz-Zygmund-type inequalities, trigonometric interpolation on non-uniform grids and unconditional Schauder bases in Besov spaces on the torus

by    K.V. Runovskii, W. Sickel

Preprint series: 97-06, Analysis

The paper is published: ZAA, 16, 669-687, 1997.

MSC:
46E35 Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems
42A15 Trigonometric interpolation
41A25 Rate of convergence, degree of approximation
41A27 Inverse theorems
42A05 Trigonometric polynomials, inequalities, extremal problems

Abstract: 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 basis.


Keywords: trigonometric interpolation, unconditional bases, Besov spaces

Upload: 1999-02-10

Update: 1999-04-07


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