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

概要

論文の詳細を見る
In this paper, we give a natural, and generalized reverse Hölder inequality, which says that if ωi ∈ A∞, then for every cube Q,∫Q∏mi=1ωiθi ≥ ∏mi=1(∫Qωi/[ωi]A∞)θiwhere ∑i=1mθi = 1, 0 ≤ θi ≤ 1.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.