Sharp Kolmogorov-type inequalities for norms of fractional derivatives of multivariate functions

Let be the space of bounded and continuous functions equipped with the norm and let e j , j = 1,…, m , be a standard basis in : Given moduli of continuity ω j , j = 1,…, m , denote We obtain new sharp Kolmogorov-type inequalities for the norms of mixed fractional derivatives of functions . Some appl...

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Bibliographic Details
Published in:Ukrainian mathematical journal 2010-10, Vol.62 (3), p.343-357
Main Authors: Babenko, V. F., Parfinovych, N.V., Pichugov, S. A.
Format: Article
Language:English
Subjects:
Algebra
Analysis
Applications of Mathematics
Geometry
Mathematics
Mathematics and Statistics
Statistics
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Summary:Let be the space of bounded and continuous functions equipped with the norm and let e j , j = 1,…, m , be a standard basis in : Given moduli of continuity ω j , j = 1,…, m , denote We obtain new sharp Kolmogorov-type inequalities for the norms of mixed fractional derivatives of functions . Some applications of these inequalities are presented.
ISSN:0041-5995
1573-9376
DOI:10.1007/s11253-010-0358-y