Abstract:Suppose that X, Y are Hilbert-space-valued continuous-path martingales such that Y is differentially subordinate to X. The paper contains the proof of sharp estimates between p-th moments of Y and the maximal function of X for 0 < p < 1. The proof rests on Burkholder's method and exploits a certain special function of three variables, enjoying appropriate size and concavity requirements. The analysis reveals an unexpected phase transition between the cases 0 < p < 1/2 and 1/2 ≤ p < 1. The latter case is relati… Show more
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