Littlewood–Paley -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