Let (X,ℱ,μ) be a
σ-finite measure space and Γ = (𝜃t: t ≧ 0) a measurable semiflow of measure
preserving transformations on (X,ℱ,μ). The maximal function f∗ of a function
f ∈ L1(μ) + L∞(μ) is defined by
The purpose of this paper is to prove that if μ(X) = ∞ and the semiflow Γ is
conservative and ergodic then for every constant α > 0