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Kolmogorov type inequalities for hypersingular integrals with homogeneous characteristic. (English) Zbl 1131.26010
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.
MSC:
26D10Inequalities involving derivatives, differential and integral operators
41A17Inequalities in approximation (Bernstein, Jackson, Nikol’skiĭ-type inequalities)
41A44Best constants (approximations and expansions)