EN
Let 𝔾 be a homogeneousgroup on ℝⁿ whose multiplication and inverse operations are polynomial maps. In 1999, T. Tao proved that the singular integral operator with Llog⁺L function kernel on ≫ is both of type (p,p) and of weak type (1,1). In this paper, the same results are proved for the Littlewood-Paley g-functions on 𝔾