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Ukrainian Mathematical Journal

, Volume 64, Issue 5, pp 721–736 | Cite as

Inequalities for derivatives of functions on an axis with nonsymmetrically bounded higher derivatives

  • V. A. Kofanov
Article

For nonperiodic functions \( x\in L_{\infty}^r(R) \) defined on the entire real axis, we prove analogs of the Babenko inequality. The obtained inequalities estimate the norms of derivatives \( \left\| {x_{\pm}^{(k) }} \right\|{L_{q[a,b] }} \) on an arbitrary interval [a, b] ⊂ R such that x (k)(a) = x (k)(b) = 0 via local L p -norms of the functions x and uniform nonsymmetric norms of the higher derivatives x(r) of these functions.

Keywords

Arbitrary Function Comparison Theorem High Derivative Yield Inequality Account Relation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 2012

Authors and Affiliations

  • V. A. Kofanov
    • 1
  1. 1.Dnepropetrovsk National UniversityDnepropetrovskUkraine

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