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Zbl 1131.26010
Babenko, Vladislav F.; Churilova, Mariya S.
Kolmogorov type inequalities for hypersingular integrals with homogeneous characteristic. (English)
[J] Banach J. Math. Anal. 1, No. 1, 66-77, electronic only (2007). ISSN 1735-8787/e

In this paper the authors establish new sharp Kolmogorov type inequalities for hypersingular integrals with homogeneous characteristic of multivariate functions from Hölder spaces. Applications of the results obtained to solve Stechkin's problem on the best approximation of unbounded hypersingular integral operator by unbounded ones on functional classes, which are defined by a majorant of the modulus of continuity, are given.
[James Adedayo Oguntuase (Abeokuta)]

MSC 2000:: *26D10 Inequalities involving derivatives, diff. and integral operators
41A17 Inequalities in approximation
41A44 Best constants

Keywords: Inequality of Kolmogorov type; hypersingular integrals; approximation of operators

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