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Monotonicity of certain functionals under rearrangement

Adriano GarsiaEugène Rodemich — 1974

Annales de l'institut Fourier

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 Ψ f ( x ) - f ( y ) p ( x - y ) d x d y < where Ψ ( u ) and p ( u ) are monotone increasing functions of | u | . Several applications are also derived. In particular these methods are shown to yield a new condition for path continuity of general stochastic processes

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