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The aim of this paper is to establish several necessary and sufficient conditions in order that the weighted inequality ρ(M f > λ)Φ(λ) ≤ C ∫_Ω~Ψ (C|f|)σdμ,λ > 0 or ρ(Mf>λ) ≤ C∫-Ω~Φ(Cλ~-1 |f|)σdμ,λ >0 holds for every uniformly integral martin