Weighted mixed weak-type inequalities for multilinear operators

KANGWEI LI; SHELDY OMBROSI; BELEN PICARDI

STUDIA MATHEMATICA

POLISH ACAD SCIENCES INST MATHEMATICS

Lugar: VARSOVIA; Año: 2018

0039-3223

In this paper we present a theorem that generalizes Sawyer´s classic result about mixed weighted inequalities to the multilinear context. Let w⃗ =(w1,...,wm) and ν=w1m1...w1mm, the main result of the paper sentences that under different conditions on the weights we can obtain‖‖‖‖T(f⃗ )(x)v‖‖‖‖L1m,∞(νv1m)≤C ∏i=1m‖fi‖L1(wi),where T is a multilinear Calder´on-Zygmund operator. To obtain this result we first prove it for the m-fold product of the Hardy-Littlewood maximal operator M, and also for (f⃗ )(x): the multi(sub)linear maximal function introduced in cite{LOPTT}. As an application we also prove a vector-valued extension to the mixed weighted weak-type inequalities of multilinear Calder´on-Zygmund operators.