Geodesic
Mean values of convexly arranged numbers and monotone rearrangements in reverse integral inequalities
Bollettino della Unione matematica italiana, Série 8, 8B (2005) no. 3, pp. 737-764.

Voir la notice de l'article provenant de la source Biblioteca Digitale Italiana di Matematica

We analyse mean values of functions with values in the boundary of a convex two-dimensional set. As an application, reverse integral inequalities imply exactly the same inequalities for the monotone rearrangement. Sharp versions of the classical Gehring lemma, the Gurov-Resetnyak theorem and the Muckenhoupt theorem are obtained.
Si studiano medie di funzioni con valori sulla frontiera di un insieme convesso bidimensionale. Come applicazione si prova che disuguaglianze integrali inverse implicano esattamente le stesse disuguaglianze per il riordinamento monotono. Si ottengono quindi versioni ottimali del classico lemma di Gehring, del teorema di Gurov-Reshetnyak e del teorema di Muckenhoupt. 
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Clemens, Werner. Mean values of convexly arranged numbers and monotone rearrangements in reverse integral inequalities. Bollettino della Unione matematica italiana, Série 8, 8B (2005) no. 3, pp. 737-764. http://geodesic.mathdoc.fr/item/BUMI_2005_8_8B_3_a13/

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