Marcinkiewicz integrals on weighted weak Hardy spaces

We prove that,under the condition ω ∈ lipα,marcinkiewicz integral μω is bounded from weighted weak hardy space whw p (rn) to weighted weak lebesgue space whw p (rn) for max {n/(n + 1/2),n/(n + α)} < p ≤ 1,where w belongs to the muckenhoupt weight class. we also give weaker smoothness condition assumed on to imply the boundedness of μ ω from whw 1 (ℝn) to wl w 1 (rn). © 2014 yue hu and yueshan wang.