One Inequality of the Landau–Kolmogorov Type for Periodic Functions of Two Variables

We obtain a new sharp inequality of the Landau–Kolmogorov type for a periodic function of two variables estimating the convolution of the best uniform approximations of its partial primitives by the sums of functions of single variable via the L ∞ -norm of the function itself and uniform norms of it...

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Bibliographic Details
Published inUkrainian mathematical journal Vol. 71; no. 2; pp. 179 - 189
Main Author Babenko, V. F.
Format Journal Article
LanguageEnglish
Published New York Springer US 01.07.2019
Springer
Springer Nature B.V
Subjects
Algebra
Analysis
Applications of Mathematics
Convolution
Equality
Geometry
Inequality
Mathematical analysis
Mathematics
Mathematics and Statistics
Norms
Periodic functions
Statistics
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Summary:We obtain a new sharp inequality of the Landau–Kolmogorov type for a periodic function of two variables estimating the convolution of the best uniform approximations of its partial primitives by the sums of functions of single variable via the L ∞ -norm of the function itself and uniform norms of its mixed primitives. Some applications of the obtained inequality are also presented.
ISSN:0041-5995
1573-9376
DOI:10.1007/s11253-019-01637-4