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arXiv · 1007.0445

Weighted inequalities for multilinear potential operators and its commutators

Ana Bernardis·Osvaldo Gorosito·Gladis Pradolini
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Abstract

We prove weighted strong inequalities for the multilinear potential operator ${\cal T}_ϕ$ and its commutator, where the kernel $ϕ$ satisfies certain growth condition. For these operators we also obtain Fefferman-Stein type inequalities and Coifman type estimates. On the other hand we prove weighted weak type inequalities for the multilinear maximal operator $\mathcal{M}_{φ,B}$ associated to a essentially nondecreasing function $φ$ and to a submultiplicative Young function $B$. This result allows us to obtain a weighted weak type inequality for the operator ${\cal T}_ϕ$.

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Ana Bernardis, Osvaldo Gorosito, Gladis Pradolini. 2010-07-02. Weighted inequalities for multilinear potential operators and its commutators. https://arxiv.org/abs/1007.0445

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