Weighted inequalities for multilinear potential operators and its commutator

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. On the other hand we prove weighted weak type inequalities for the multilinear maximal operator $mathcal{M}_{varphi,B}$ associated to a essentially nondecreasing function $arphi$ and to a submultiplicative Young function $B$. This result allows us to obtain a weighted weak type inequality for the operator ${cal T}_{phi}$ %by using a weak control estimate between this operator %and $mathcal{M}_{arphi,B}$ for appropriated functions $arphi$ %and $B$.