{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/86815"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/86815","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"A Weak Type Inequality for Martingale Transforms and Other Subordinate Martingales","abstract":"We study a problem of finding the best constant in a weak type inequality for martingale transforms extending the result of Burkholder (1966). First, we study the inequality for the discrete-time martingale case. We present examples of martingales that give good lower estimates of the best constant. We then find a biconcave function to prove that the supremum of these lower estimates is in fact the best constant. 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First, we study the inequality for the discrete-time martingale case. We present examples of martingales that give good lower estimates of the best constant. We then find a biconcave function to prove that the supremum of these lower estimates is in fact the best constant. We use this biconcave function to prove a sharp weak type inequality for differentially subordinate martingales with the same best constant, and by approximation a similar inequality for stochastic integrals. We generalize these results to the continuous-time case and give an application to harmonic functions.","Made available in DSpace on 2015-09-28T15:19:40Z (GMT). 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