## Banach Journal of Mathematical Analysis

### Kolmogorov type inequalities for hypersingular integrals with homogeneous characteristic

#### 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

#### 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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