The Equivalence Relations between the Ditzian–Totik Moduli of Smoothness and Best Polynomial Approximation in the Besov Spaces

Li, Song

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Publication date

November 1997

DOI

10.1006/jmaa.1997.5591

Publisher

Academic Press.

Abstract

AbstractThe best polynomial approximation is closely related to the Ditzian–Totik modulus of smoothness. In 1988, Z. Ditzian and V. Totik gave some equivalences between them and the class of Besov-type spacesBα,spwith 1≤p≤∞ and 1≤s≤∞. We extend these equivalences to the similar Besov-type spaces with 0<s<1. We also give some new equivalences by means of the behavior of best polynomial approximation

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The Equivalence Relations between the Ditzian–Totik Moduli of Smoothness and Best Polynomial Approximation in the Besov Spaces

Abstract

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The Equivalence Relations between the Ditzian–Totik Moduli of Smoothness and Best Polynomial Approximation in the Besov Spaces

Abstract

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