Monotonicity of certain functionals under rearrangement

Type: Article

Publication Date: 1974-01-01

Citations: 90

DOI: https://doi.org/10.5802/aif.507

Abstract

We show here that a wide class of integral inequalities concerning functions on [0,1] can be obtained by purely combinatorial methods. More precisely, we obtain modulus of continuity or other high order norm estimates for functions satisfying conditions of the type ∫ 0 1 ∫ 0 1 Ψf(x)-f(y) p(x-y)dxdy<∞ where Ψ(u) and p(u) are monotone increasing functions of |u|.

Locations

  • French digital mathematics library (Numdam) - View - PDF
  • Annales de l’institut Fourier - View - PDF

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