Marcinkiewicz Integrals on Weighted Weak Hardy Spaces - Yue Hu; Yueshan Wang (Journal of Function Spaces)
We prove that, under the condition Ω∈Lipα, Marcinkiewicz integral μΩ is bounded from weighted weak Hardy space WHwpRn to weighted weak Lebesgue space WLwpRn for maxn/n+1/2,n/n+α<p≤1, where w belongs to the Muckenhoupt weight class. We also give weaker smoothness condition assumed on Ω to imply the boundedness of μΩ from WHw1ℝn to WLw1Rn.