Nous montrons qu’une large classe d’inégalités intégrales concernant des fonctions sur peut être obtenue par des méthodes purement combinatoires. De façon plus précise, nous obtenons des modules de continuité ou d’autres estimations de normes d’ordre élevé pour des fonctions vérifiant des conditions du type
où et sont des fonctions croissantes de . On en déduit différentes applications. On montre en particulier que ces méthodes donnent une nouvelle condition pour la continuité des chemins d’un processus stochastique général.
We show here that a wide class of integral inequalities concerning functions on 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 where and are monotone increasing functions of .
Several applications are also derived. In particular these methods are shown to yield a new condition for path continuity of general stochastic processes
@article{AIF_1974__24_2_67_0, author = {Garsia, Adriano and Rodemich, Eug\`ene}, title = {Monotonicity of certain functionals under rearrangement}, journal = {Annales de l'Institut Fourier}, pages = {67--116}, publisher = {Institut Fourier}, address = {Grenoble}, volume = {24}, number = {2}, year = {1974}, doi = {10.5802/aif.507}, mrnumber = {54 #2894}, zbl = {0274.26006}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/aif.507/} }
TY - JOUR AU - Garsia, Adriano AU - Rodemich, Eugène TI - Monotonicity of certain functionals under rearrangement JO - Annales de l'Institut Fourier PY - 1974 SP - 67 EP - 116 VL - 24 IS - 2 PB - Institut Fourier PP - Grenoble UR - http://archive.numdam.org/articles/10.5802/aif.507/ DO - 10.5802/aif.507 LA - en ID - AIF_1974__24_2_67_0 ER -
%0 Journal Article %A Garsia, Adriano %A Rodemich, Eugène %T Monotonicity of certain functionals under rearrangement %J Annales de l'Institut Fourier %D 1974 %P 67-116 %V 24 %N 2 %I Institut Fourier %C Grenoble %U http://archive.numdam.org/articles/10.5802/aif.507/ %R 10.5802/aif.507 %G en %F AIF_1974__24_2_67_0
Garsia, Adriano; Rodemich, Eugène. Monotonicity of certain functionals under rearrangement. Annales de l'Institut Fourier, Tome 24 (1974) no. 2, pp. 67-116. doi : 10.5802/aif.507. http://archive.numdam.org/articles/10.5802/aif.507/
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