Monotonicity of certain functionals under rearrangement

Adriano Garsia; Eugène Rodemich

Annales de l'institut Fourier (1974)

  • Volume: 24, Issue: 2, page 67-116
  • ISSN: 0373-0956

Abstract

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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

How to cite

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Garsia, Adriano, and Rodemich, Eugène. "Monotonicity of certain functionals under rearrangement." Annales de l'institut Fourier 24.2 (1974): 67-116. <http://eudml.org/doc/74178>.

@article{Garsia1974,
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 $\int ^1_0\int ^1_0\Psi \big (\{f(x)-f(y)\over p(x-y)\}\big )dxdy&lt; \infty $ where $\Psi (u)$ and $p(u)$ are monotone increasing functions of $\vert u\vert $.Several applications are also derived. In particular these methods are shown to yield a new condition for path continuity of general stochastic processes},
author = {Garsia, Adriano, Rodemich, Eugène},
journal = {Annales de l'institut Fourier},
language = {eng},
number = {2},
pages = {67-116},
publisher = {Association des Annales de l'Institut Fourier},
title = {Monotonicity of certain functionals under rearrangement},
url = {http://eudml.org/doc/74178},
volume = {24},
year = {1974},
}

TY - JOUR
AU - Garsia, Adriano
AU - Rodemich, Eugène
TI - Monotonicity of certain functionals under rearrangement
JO - Annales de l'institut Fourier
PY - 1974
PB - Association des Annales de l'Institut Fourier
VL - 24
IS - 2
SP - 67
EP - 116
AB - 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 $\int ^1_0\int ^1_0\Psi \big ({f(x)-f(y)\over p(x-y)}\big )dxdy&lt; \infty $ where $\Psi (u)$ and $p(u)$ are monotone increasing functions of $\vert u\vert $.Several applications are also derived. In particular these methods are shown to yield a new condition for path continuity of general stochastic processes
LA - eng
UR - http://eudml.org/doc/74178
ER -

References

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Citations in EuDML Documents

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  1. Matthias Kurzke, A nonlocal singular perturbation problem with periodic well potential
  2. Matthias Kurzke, A nonlocal singular perturbation problem with periodic well potential
  3. G. Pisier, Conditions d'entropie assurant la continuité de certains processus et applications à l'analyse harmonique
  4. Constantin Nanopoulos, Photis Nobelis, Régularité et propriétés limites des fonctions aléatoires
  5. Talenti, Giorgio, Inequalities in rearrangement invariant function spaces
  6. Kolyada, Viktor I., On embedding theorems
  7. Guido Trombetti, Metodi di simmetrizzazione nelle equazioni alle derivate parziali

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