Estimates for multilinear singular integral operators with nonsmooth kernels (Q1758570)

Let \(\mathcal{H}\) be a set and let \(d\) be a quasi-metric satisfying that there exists a constant \(\mathrm{k} \leq 1\) such that for all \(x, y, z \in \mathcal{H}\) \[ d(x,y) \leq \mathrm{k} \;[d(x,z) + d(y,z)]. \] Let \(\mu\) be a positive Borel measure on \(\mathcal{H}\). Let \((\mathcal{H}, d, \mu)\) be a space of homogeneous type in the sense of \textit{R. H. Coifman} and \textit{G. Weiss} [``Analyse harmonique non-commutative sur certains espaces homogènes''. Lecture Notes in Mathematics. 242. Berlin-Heidelberg-New York: Springer-Verlag. (1971; Zbl 0224.43006)]. The authors consider the mapping properties on \(L^{p_1}(\mathcal{H}) \times \cdots \times L^{p_m}(\mathcal{H})\) for the multilinear singular integral operators with nonsmooth kernels under suitable conditions.