Weighted inequalities for multilinear potential operators and their commutators

ANA BERNARDIS; OSVALDO GOROSITO; GLADIS PRADOLINI

POTENTIAL ANALYSIS

SPRINGER

Año: 2011 vol. 35 p. 253 - 274

0926-2601

We prove weighted strong inequalities for the multilinear potential operator ${cal T}_{phi}$ and its commutator, where the kernel $phi$ satisfies certain growth condition. For these operators we also obtain Fefferman-Stein type inequalities and Coifman type estimates. Moreover we prove weighted weak type inequalities for the multilinear maximal operator $mathcal{M}_{varphi,L^{B}}$ associated to an essentially nondecreasing function $varphi$ and to the Orlicz space $L^{B}$ for a given Young function $B$. This result allows us to obtain a weighted weak type inequality for the operator ${cal T}_{phi}$.