Geodesic
Power means and the reverse Hölder inequality
Victor D. Didenko 1   ; Anatolii A. Korenovskyi 2
1 University of Brunei Darussalam BE1410 Bandar Seri Begawan, Brunei
2 Odessa I. I. Mechnikov National University Dvoryanskaya 2 65026 Odessa, Ukraine
Studia Mathematica, Tome 207 (2011) no. 1, pp. 85-95 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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 $0\alpha\beta$. In the present paper, sharp estimates of the compositions of the power means $\mathcal{P}_\alpha w(x):=((1/x)\int_0^x w^\alpha(t)\,dt)^{1/\alpha}$, $x>0$, are obtained for various exponents $\alpha$. As a result, for the function $w$ a property of self-improvement of summability exponents is established.
DOI : 10.4064/sm207-1-6
Keywords: non negative measurable function defined positive semi axis satisfying reverse lder inequality exponents alpha beta present paper sharp estimates compositions power means mathcal alpha int alpha alpha obtained various exponents alpha result function property self improvement summability exponents established

Victor D. Didenko  1   ; Anatolii A. Korenovskyi  2

1 University of Brunei Darussalam BE1410 Bandar Seri Begawan, Brunei
2 Odessa I. I. Mechnikov National University Dvoryanskaya 2 65026 Odessa, Ukraine 
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Victor D. Didenko; Anatolii A. Korenovskyi. Power means and the reverse Hölder inequality. Studia Mathematica, Tome 207 (2011) no. 1, pp. 85-95. doi: 10.4064/sm207-1-6

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