Banach Journal of Mathematical Analysis

Kolmogorov type inequalities for hypersingular integrals with homogeneous characteristic

Vladislav F. Babenko and Mariya S. Churilova

Full-text: Open access

Abstract

New sharp Kolmogorov type inequalities for hypersingular integrals with homogeneous characteristic of multivariate functions from Holder spaces are obtained. Proved inequalities are used to solve the Stechkin's problem on the best approximation of unbounded hypersingular integral operator by bounded ones on functional classes which are defined by a majorant of the modulus of continuity.

Article information

Source
Banach J. Math. Anal., Volume 1, Number 1 (2007), 66-77.

Dates
First available in Project Euclid: 21 April 2009

Permanent link to this document
https://projecteuclid.org/euclid.bjma/1240321556

Digital Object Identifier
doi:10.15352/bjma/1240321556

Mathematical Reviews number (MathSciNet)
MR2350195

Zentralblatt MATH identifier
1131.26010

Subjects
Primary: 26D10: Inequalities involving derivatives and differential and integral operators
Secondary: 41A17: Inequalities in approximation (Bernstein, Jackson, Nikol s kii-type inequalities) 41A44: Best constants

Keywords
inequality of Kolmogorov type hypersingular integrals approximation of operators

Citation

Babenko, Vladislav F.; Churilova, Mariya S. Kolmogorov type inequalities for hypersingular integrals with homogeneous characteristic. Banach J. Math. Anal. 1 (2007), no. 1, 66--77. doi:10.15352/bjma/1240321556. https://projecteuclid.org/euclid.bjma/1240321556


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References

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