Homogeneous spaces adapted to singular integral operators involving rotations

摘要: Calder\'on-Zygmund decompositions of functions have been used to prove weak-type (1,1) boundedness singular integral operators. In many examples, the decomposition is done with respect a family balls that corresponds some dilations. We study operators $T$ require more particular families balls, providing new spaces homogeneous type. Rotations play decisive role in construction these balls. Boundedness can then be shown via this space and $\LP^p$ estimates for acting on $\LP^p(G)$, where $G$ Lie group. Our results apply setting underlying group Heisenberg rotations are symplectic automorphisms. They also arise from hydrodynamical problem involving rotations.