Power means and the reverse Hölder inequality
Victor D. Didenko ; Anatolii A. Korenovskyi
Studia Mathematica, Tome 204 (2011), p. 85-95 / Harvested from The Polish Digital Mathematics Library
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Let w be a non-negative measurable function defined on the positive semi-axis and satisfying the reverse Hölder inequality with exponents 0 < α < β. In the present paper, sharp estimates of the compositions of the power means αw(x):=((1/x)∫0xwα(t)dt)1/α, x > 0, are obtained for various exponents α. As a result, for the function w a property of self-improvement of summability exponents is established.

Publié le : 2011-01-01
EUDML-ID : urn:eudml:doc:285529 
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     title = {Power means and the reverse H\"older inequality},
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Victor D. Didenko; Anatolii A. Korenovskyi. Power means and the reverse Hölder inequality. Studia Mathematica, Tome 204 (2011) pp. 85-95. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm207-1-6/