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October, 2012 Multilinear version of reversed Hölder inequality and its applications to multilinear Calderón-Zygmund operators
Qingying XUE, Jingquan YAN
J. Math. Soc. Japan 64(4): 1053-1069 (October, 2012). DOI: 10.2969/jmsj/06441053

Abstract

In this paper, we give a natural, and generalized reverse Hölder inequality, which says that if $\omega_{i}\in A_\infty$, then for every cube $Q$, \begin{equation} \int_Q\prod_{i =1}^m{\omega_i}^{\theta_i} \geq \prod_{i = 1}^m \left( \frac{\int_Q{\omega_i}}{[\omega_i]_{A_\infty}} \right)^{\theta_i}, \end{equation} where $\sum_{i=1}^m\theta_{i}=1$, $0\leq\theta_i\leq1$.

As a consequence, we get a more general inequality, which can be viewed as an extension of the reverse Jensen inequality in the theory of weighted inequalities. Based on this inequality (0.1), we then give some results concerning multilinear Calderón-Zygmund operators and maximal operators on weighted Hardy spaces, which improve some known results significantly.

Citation

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Qingying XUE. Jingquan YAN. "Multilinear version of reversed Hölder inequality and its applications to multilinear Calderón-Zygmund operators." J. Math. Soc. Japan 64 (4) 1053 - 1069, October, 2012. https://doi.org/10.2969/jmsj/06441053

Information

Published: October, 2012
First available in Project Euclid: 29 October 2012

zbMATH: 1263.47012
MathSciNet: MR2998916
Digital Object Identifier: 10.2969/jmsj/06441053

Subjects:
Primary: 47A30
Secondary: 42B20

Rights: Copyright © 2012 Mathematical Society of Japan

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Vol.64 • No. 4 • October, 2012
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