Document Type
Article
Peer Reviewed
1
Publication Date
2012
Scholarship Domain(s)
Scholarship of Discovery
Abstract
Given a sequence of martingale differences, Burkholder found the
sharp constant for the Lp-norm of the corresponding martingale transform. We
are able to determine the sharp Lp-norm of a small "quadratic perturbations"
of the martingale transform in Lp. By "quadratic perturbation" of the martin-
gale transform we mean the Lp norm of the square root of the squares of the
martingale transform and the original martingale (with small constant). The
problem of perturbation of martingale transform appears naturally if one wants
to estimate the linear combination of Riesz transforms (as, for example, in the
case of Ahlfors{Beurling operator).
Recommended Citation
Boros, Nicholas; Janakiraman, Prabhu; and Volberg, Alexander, "Perturbation of Burkholder's Martingale Transform and Monge-Ampère Equation" (2012). Faculty Scholarship – Mathematics. 4.
https://digitalcommons.olivet.edu/math_facp/4
Comments
Advances in Mathematics 230(s 4–6):2198–2234. DOI:10.1016/j.aim.2012.03.035