Integral Inequalities for Equimeasurable Rearrangements

Duff, G. F. D.

Canadian journal of mathematics, Tome 22 (1970) no. 2, pp. 408-430

Résumé

For a real-valued function f on the domain [0,b], the equimeasurable decreasing rearrangement f* of f is defined as a function μ –1 inverse to μ, where μ(y) is the measure of the set {x|f(x) > y}. Inequalities connected with rearrangements of sequences as well as functions play a considerable part in various branches of analysis, and, for example, the concluding chapter of Hardy, Littlewood, and Pólya [3] is devoted to rearrangement inequalities. Equimeasurable rearrangements of functions are also used by Zygmund [6, Vol. II, Chapters I and XII].

Détail

DOI : 10.4153/CJM-1970-050-1

Bibliographie

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