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Sharp Lower bound estimates for vector-valued and matrix-valued multipliers in
Nicholas Boros, Alexander Volberg
We generalize the idea of a multiplier in two different ways and generalize a recent result of Geiss, Montomery-Smith and Saksman. First of all, we consider multipliers in the form…
The Operator Norm of a Quadratic Perturbation of the Real Part of the Ahlfors--Beurling Operator
Nicholas Boros, László Székelyhidi, Alexander Volberg
We will explain how to compute the exact operator norm of a "quadratic perturbation" of the real part of the Ahlfors--Beurling operator. For the lower bound estimate we use a…
Laminates Meet Burkholder Functions
Nicholas Boros, Laszlo Szekelyhidi, Alexander Volberg
We will explain how to compute the exact operator norm of a "quadratic perturbation" of the real part of the Ahlfors--Beurling operator. For the lower bound estimate we use a…
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…