Give the definition of Littlewood Paley operator on spaces of homogeneous type and prove that the image of a BMO function under this operator is either equal to infinity almost everywhere or is in BMO.

• 给出了齐型空间上 Littlewood- Paley算子 G的定义 ,证明了当 f是 BMO函数时 ,G( f )或者几乎处处等于无穷 ; 或者其 BMO范数被 f的 BMO范数控制