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Generalized Rearrangement Inequalities

The American Mathematical Monthly, 2001
(2001). Generalized Rearrangement Inequalities. The American Mathematical Monthly: Vol. 108, No. 2, pp. 158-165.
Robert Geretschläger, Walther Janous
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Rearrangement inequalities

Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 1980
SynopsisRearrangement inequalities of Ruderman and Minc are generalized.
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Integral Inequalities for Equimeasurable Rearrangements

Canadian Journal of Mathematics, 1970
For a real-valued functionfon the domain [0,b], the equimeasurable decreasing rearrangementf* offis defined as a functionμ–1inverse toμ, whereμ(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 ...
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Rearrangement Inequalities for Littlewood-Paley Operators

Mathematische Nachrichten, 1987
Let \(f^*_ w(t)=\inf \{\lambda >0;w(\{x\in {\mathbb{R}}^ n;| f(x)| >\ell \})\leq t\}\) be the non-decreasing rearrangement of f with respect to a weight w, Mf be the Hardy-Littlewood maximal function of f, and \(M_ qf=M(| f|^ q)^{1/q}.\) The author shows for \(w\in A_{\infty}\).
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Local Khintchine inequality in rearrangement invariant spaces

Annali di Matematica Pura ed Applicata (1923 -), 2013
This paper is devoted to analyse the local version of the Kinchin inequality in rearrangement invariant (r.i.)\ Banach function spaces. An r.i.\ space \(X\) satisfies this property if there are constants \(\alpha, \beta >0\) such that for every measurable set \(E \subset [0,1]\) with \(m(E) >0\) there exists \(N:=N(E)\) such that \[ \alpha \varphi_X(m ...
Astashkin, Serguey V.   +1 more
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