✦ LIBER ✦

Strong Converse Inequalities

✍ Scribed by V. Totik

Publisher: Elsevier Science
Year: 1994
Tongue: English
Weight: 188 KB
Volume: 76
Category: Article
ISSN: 0021-9045
DOI: 10.1006/jath.1994.1023

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✦ Synopsis

Converse inequalities are proved for a family of operators that state the equivalence of two terms of error in approximation to the revelant modulus of smoothness. Such inequalities have been proved by Z. Ditzian and K. G. Ivanov with a different method. Our emphasis is that these so-called strong converse inequalities follow from some standard estimates on the derivatives of the operators without additional work; hence we extend the Ditzian-Ivanov result to a large family of operators. The method of the paper is very close in spirit to the classical parabola technique. 1994 Academic Press, Inc.

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