Endpoint learning for multilinear commutator of singular integral on space of homogeneous type

In this paper, we prove the endpoint estimates for the multilinear commutator related to the singular integral on the space of homogeneous type by means of the L^p (l <; p <; ∞) boundedness for the singular integral operator. The main tools of the proof are decomposition of function spaces and some general inequalities. The estimates we established are widely applied in support vector machines, especially the Minkowski´s inequality and Holde´s inequality which may have application to classification problems based on Kernel methods.