Littlewood–Paley $g$-functions with rough kernels on homogeneous groups
Volume 195 / 2009
Studia Mathematica 195 (2009), 51-86
MSC: Primary 42B25; Secondary 43A80, 43A99.
DOI: 10.4064/sm195-1-4
Abstract
Let $\mathbb G$ be a homogeneousgroup on ${\mathbb R}^n$ whose multiplication and inverse operations are polynomial maps. In 1999, T. Tao proved that the singular integral operator with $L\log^+\!\!L$ function kernel on $\gg$ 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 $\mathbb G$
