| Littlewood-Paley operators, g-function, s-function and gλ*-function (λ>3),considered as operators on the space of functions of weighted bounded mean oscillation BMOw ((BMO)w), are "bounded operators". Exactly, we proved that if f BMOw((BMO)w) and | {x:Tf(x)≠∞|>0; then Tf is also in BMOw((BMO) and there is a constant C independent of f such that ‖Tf‖BMOwBMOw(‖Tf‖BMOw(BMO)w),where T is one of those Littlewood-Paley operators. |
