Abstract
We find the sharp constant of the inequality , where is the transform of a martingale under a predictable sequence with absolute value 1, , and is any real number.
Information
Received: 8 March 2014; Revised: 1 February 2015; Accepted: 25 March 2015; Published: 2015
First available in Project Euclid: 16 November 2017
Digital Object Identifier: 10.2140/apde.2015.8.765
Subjects:
Primary:
42B20
,
42B35
,
47A30
Keywords:
Bellman function
,
concave envelopes
,
developable surface
,
least concave function
,
martingale inequalities
,
martingale transform
,
Monge–Ampère equation
,
torsion
Rights: Copyright © 2015 Mathematical Sciences Publishers