Results in Mathematics

, Volume 24, Issue 1–2, pp 153–160 | Cite as

Weighted norm inequalities for the quasi-derivatives of ordinary differential operators

  • M. Möller
  • A. Zettl


For a compact interval I of the real line and for 1 ≤ p < ∞ the classical inequality
$$\int_{I}\mid y^{(k)}\mid^{p}\ dx \leq \varepsilon\int_{I}\mid y^{(n)}\mid^{p}\ dx +K(\varepsilon)\int_{I}\mid y\mid^{p} dx$$
is extended by replacing y(n) by the action of an n-th order quasi-differential operator and y(k) by the corresponding k-th quasi-derivative for 0 ≤+ k < n. Also quite general weight functions are allowed.

1991 AMS subject classification

34A40 26D10 34L99 

Key words and phrases

apriori inequalities quasi-derivatives integral inequalities with weights 


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    A. Zettl, Formally self-adjoint quasi-differential operators, Rocky Mountain J. Math., 5 (1975), 453–474.MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Birkhäuser Verlag, Basel 1993

Authors and Affiliations

  • M. Möller
    • 1
  • A. Zettl
    • 1
  1. 1.Northern Illinois UniversityDeKalbUSA

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