Marcinkiewicz Integrals on Weighted Weak Hardy Spaces

Abstract EN

We prove that, under the condition Ω ∈ Lip α , Marcinkiewicz integral μ Ω is bounded from weighted weak Hardy space W H w p R n to weighted weak Lebesgue space W L w p R n for m a x 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 Ω to imply the boundedness of μ Ω from W H w 1 ℝ n to W L w 1 R n .