Abstract
In this paper, we introduce multilinear geometric mean Hörmander conditions to prove multilinear Calderón-Zygmund theory. It requires weaker assumptions comparing our kernel conditions with the geometric Hörmander conditions. Crucially, the approach relies on the Calderón-Zygmund decomposition and deals with the bad part by a certain convolution function. The endpoint estimates for multilinear Littlewood-Paley operators are also given.
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