Weighted inequalities for multilinear potential operators and its commutators

Abstract

We prove weighted strong inequalities for the multilinear potential operator ${\mathcal{T}}_{\varphi }$ and its commutator, where the kernel $\varphi$ 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 ${\mathcal{M}}_{\phi ,B}$ associated to a essentially nondecreasing function $\phi$ and to a submultiplicative Young function $B$. This result allows us to obtain a weighted weak type inequality for the operator ${\mathcal{T}}_{\varphi }$.

Cited by in corpus (1)

• Weighted Estimates for the iterated Commutators of Multilinear Maximal and Fractional Type Operators