14 citations · 17 across the 5 of their papers we have counts for
6 papers
Dimension for Martingales
Prabhu Janakiraman
A martingale \int H.dZ is defined as having Dimension k if H has rank k almost surely, almost all t. Dimension can be used as a geometric invariant to classify and study martingale…
Perturbation of Burkholder's martingale transform and Monge--Ampère equation
Nicholas Boros, Prabhu Janakiraman, Alexander Volberg
Let be a complex martingale difference in where and $\{\e_k\}_{k \geq 0}$ a sequence in We obtain the following generali…
Subordination by orthogonal martingales in
Prabhu Janakiraman, Alexander Volberg
We are given two martingales on the filtration of the two dimensional Brownian motion. One is subordinated to another. We want to give an estimate of -norm of a subordinated o…
Some new Bellman functions and subordination by orthogonal martingales in
Prabhu Janakiraman, Vasily Vasyunin, Alexander Volberg
Given two martingales on the filtration generated by two dimensional Brownian motion, we want to estimate the norm of the subordinated one if we have some extra orthogonality…
Subordination by orthogonal martingales in and zeros of Laguerre polynomials
Alexander Borichev, Prabhu Janakiraman, Alexander Volberg
In this paper we address the question of finding the best -norm constant for martingale transforms with one-sided orthogonality. We consider two martingales on a probability s…
On Burkholder function for orthogonal martingales and zeros of Legendre polynomials
Alexander Borichev, Prabhu Janakiraman, Alexander Volberg
Burkholder obtained a sharp estimate of $\E|W|^p$ via $\E|Z|^p$, where is a martingale transform of , or, in other words, for martingales differentially subordinated to…