Vol. 8, No. 4, 2015

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Inequality for Burkholder's martingale transform

Paata Ivanisvili

Vol. 8 (2015), No. 4, 765–806
Abstract

We find the sharp constant C = C(τ,p, EG, EF) of the inequality (G2 + τ2F2)12p CFp, where G is the transform of a martingale F under a predictable sequence ε with absolute value 1, 1 < p < 2, and τ is any real number.

Keywords
martingale transform, martingale inequalities, Monge–Ampère equation, torsion, least concave function, concave envelopes, Bellman function, developable surface
Mathematical Subject Classification 2010
Primary: 42B20, 42B35, 47A30
Milestones
Received: 8 March 2014
Revised: 1 February 2015
Accepted: 25 March 2015
Published: 21 June 2015
Authors
Paata Ivanisvili
Department of Mathematics
Michigan State University
619 Red Cedar Road
East Lansing, MI 48824
United States