Strong Differential Subordination and Sharp Inequalities for Orthogonal Processes

  • Adam Osękowski


We introduce a strong differential α-subordination for continuous-time processes, which generalizes this notion from the discrete-time setting, due to Burkholder and Choi. Then we determine the best constants in the L p estimates for a nonnegative submartingale and its strong α-subordinate under an additional assumption on the orthogonality of these two processes.


Martingale Submartingale Orthogonal processes Differential subordination Strong differential subordination 

Mathematics Subject Classification (2000)

60G44 60G48 


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Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Department of Mathematics, Informatics and MechanicsUniversity of WarsawWarsawPoland

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