Abstract
Let f , g be two Hilbert-space-valued martingales such that g is differentially subordinate to f . The paper contains the proof of the estimate ‖ g ‖ p , ∞ ≤ 2 p ( p + 1 ) p − 1 ‖ f ‖ p , ∞ , 1 < p < ∞ . The constant is shown to be of optimal order for p → ∞ and for p → 1 . Related results for transforms of UMD-valued martingales are also established.
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