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.
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
Affiliations des auteurs :
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
@article{10_4064_sm207_1_6,
author = {Victor D. Didenko and Anatolii A. Korenovskyi},
title = {Power means and the reverse {H\"older} inequality},
journal = {Studia Mathematica},
pages = {85--95},
year = {2011},
volume = {207},
number = {1},
doi = {10.4064/sm207-1-6},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/sm207-1-6/}
}
TY - JOUR
AU - Victor D. Didenko
AU - Anatolii A. Korenovskyi
TI - Power means and the reverse Hölder inequality
JO - Studia Mathematica
PY - 2011
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EP - 95
VL - 207
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UR - http://geodesic.mathdoc.fr/articles/10.4064/sm207-1-6/
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%J Studia Mathematica
%D 2011
%P 85-95
%V 207
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4064/sm207-1-6/
%R 10.4064/sm207-1-6
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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
