Weighted mixed weak-type inequalities for multilinear operators

Kangwei Li, Sheldy J. Ombrosi, M. Belén Picardi
2019 Studia Mathematica  
In this paper we present a theorem that generalizes Sawyer's classic result about mixed weighted inequalities to the multilinear context. Let w⃗=(w_1,...,w_m) and ν = w_1^1/m...w_m^1/m, the main result of the paper sentences that under different conditions on the weights we can obtain T(f⃗ )(x)/v_L^1/m, ∞(ν v^1/m)≤ C ∏_i=1^mf_i_L^1(w_i), where T is a multilinear Calderón-Zygmund operator. To obtain this result we first prove it for the m-fold product of the Hardy-Littlewood maximal operator M,
more » ... nd also for M(f⃗)(x): the multi(sub)linear maximal function introduced in LOPTT. As an application we also prove a vector-valued extension to the mixed weighted weak-type inequalities of multilinear Calderón-Zygmund operators.
doi:10.4064/sm170529-31-8 fatcat:tgryz46zjfddpeddgqsamqkrs4