## Journal of the Mathematical Society of Japan

### Multilinear version of reversed Hölder inequality and its applications to multilinear Calderón-Zygmund operators

#### 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 $Q$, $$\int_Q\prod_{i =1}^m{\omega_i}^{\theta_i} \geq \prod_{i = 1}^m \left( \frac{\int_Q{\omega_i}}{[\omega_i]_{A_\infty}} \right)^{\theta_i},$$ 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.

#### Article information

Source
J. Math. Soc. Japan, Volume 64, Number 4 (2012), 1053-1069.

Dates
First available in Project Euclid: 29 October 2012

https://projecteuclid.org/euclid.jmsj/1351516768

Digital Object Identifier
doi:10.2969/jmsj/06441053

Mathematical Reviews number (MathSciNet)
MR2998916

Zentralblatt MATH identifier
1263.47012

#### Citation

XUE, Qingying; YAN, Jingquan. Multilinear version of reversed Hölder inequality and its applications to multilinear Calderón-Zygmund operators. J. Math. Soc. Japan 64 (2012), no. 4, 1053--1069. doi:10.2969/jmsj/06441053. https://projecteuclid.org/euclid.jmsj/1351516768

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