© Hindawi Publishing Corp. BOUNDEDNESS OF MULTILINEAR OPERATORS ON TRIEBEL-LIZORKIN SPACES

The purpose of this paper is to study the boundedness in the context of Triebel-Lizorkin spaces for some multilinear operators related to certain convolution operators. The opera-tors include Littlewood-Paley operator, Marcinkiewicz integral, and Bochner-Riesz operator. 2000 Mathematics Subject Classification: 42B20, 42B25. 1. Introduction. Let T be a Calderon-Zygmund operator. A well-known result of Coif-man et al. [6] states that the commutator [b,T] = T(bf)−bTf (where b ∈ BMO) is bounded on Lp(Rn) for 1 < p < ∞; Chanillo [1] proves a similar result when T is re-placed by the fractional integral operator. In [7, 9], Janson and Paluszyński extend these results to the Triebel-Lizorkin spaces and the case b ∈ Lipβ (where Lipβ is th