Journal of the Mathematical Society of Japan

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

Qingying XUE and Jingquan YAN

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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.

Article information

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

First available in Project Euclid: 29 October 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 47A30: Norms (inequalities, more than one norm, etc.)
Secondary: 42B20: Singular and oscillatory integrals (Calderón-Zygmund, etc.)

reverse Hölder inequality multilinear Calderón-Zygmund operator multiple weights $A_{¥vec{p}}$ weighted Hardy type spaces


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.

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