We prove that the best so far known constant cp = p−p 1−p , p ∈ (0, 1) of a domination inequality, which originates to Lenglart, is sharp. In particular, we solve an open question posed by Revuz and Yor [12]. Motivated by the application to maximal inequalities, like e.g. the Burkholder-Davis-Gundy inequality, we also study the domination inequality under an additional monotonicity assumption. In this special case, a constant which stays bounded for p near 1 was proven by Pratelli and Lenglart. We provide the sharp constant for this case.
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