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Mean values of convexly arranged numbers and monotone rearrangements in reverse integral inequalities

Werner Clemens — 2005

Bollettino dell'Unione Matematica Italiana

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.

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