Lifted rough maximal operators satisfy optimal weak-type estimates precisely when γ ∈ ℝ\{0} (p>1) or γ ∈ (-∞,-n)∪(0,∞) (p=1, Ω∈ L(log L)), with applications to Poisson integrals and H^{1}.
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Optimal Weak-Type Estimates and Their Applications of Lifted Rough Maximal Operators
Lifted rough maximal operators satisfy optimal weak-type estimates precisely when γ ∈ ℝ\{0} (p>1) or γ ∈ (-∞,-n)∪(0,∞) (p=1, Ω∈ L(log L)), with applications to Poisson integrals and H^{1}.