Abstract
We obtain sharp estimates for some multilinear commutators related to certain sublinear integral operators. These operators include the Littlewood-Paley operator and Marcinkiewicz operator. As an application, we obtain weighted L p (p > 1) inequalities and an L log L-type estimate for multilinear commutators.
Highlights
Let b ∈ BM O(Rn) and T be the Calderon – Zygmund operator
The main purpose of this paper is to prove the sharp estimates for some multilinear commutators related to certain sublinear integral operators
We shall establish the sharp estimates for the multilinear commutators only under certain conditions on the size of the operators
Summary
The sharp estimates for some multilinear commutators related to certain sublinear integral operators are obtained. The operators include the Littlewood – Paley operator and the Marcinkiewicz operator. We obtain the weighted Lp (p > 1) inequalities and L log L-type estimate for the multilinear commutators. Одержано точнi оцiнки для деяких мультилiнiйних комутаторiв, що пов’язанi з певними сублiнiйними iнтегральними операторами. Цi оператори включають в себе оператор Лiтлвуда – Палея та оператор Марцiнкевича. Отримано зваженi Lp (p > 1) нерiвностi та оцiнку типу L log L для мультилiнiйних комутаторiв
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