On the failure of lower square function estimates in the non-homogenous weighted setting.
Recent Developments in Harmonic Analysis May 15, 2017 - May 19, 2017
Location: MSRI: Simons Auditorium
lower square function
discrete martingale transform
42B20 - Singular and oscillatory integrals (Calderón-Zygmund, etc.)
We show that the classical A_infinity condition is not sufficient for a lower square function estimate in the non-homogeneous weighted L^2 space. We also show that under the martingale A_2 condition, an estimate holds true, but the optimal power of the characteristic jumps from 1 / 2 to 1. This is in a sharp contrast to recent positive results in this direction on the discrete time non-homogeneous martingale transforms. Joint work with Domelevo, Ivanisvili, Treil, Volberg while in residence at MSRI.
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