PVSeminar #30, 17 March 2022: Rodrigo Bañuelos
Автор: PVSeminar
Загружено: 2022-03-17
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PVSeminar #30, 17 March 2022.
(https://probvic.wordpress.com/pvseminar/)
Rodrigo Bañuelos (Purdue University): Martingale transforms and discrete singular integrals
Abstract: The speaker will discuss l^p estimates (p is strictly between 1 and ∞) for a collection of discrete operators on the d-dimensional lattice Z^d, d ≥ 1, that arise from certain martingale transforms. The d = 1 case of the construction leads to the discrete Hilbert transform introduced by David Hilbert at the beginning of the 20th century. This case shows that the classical Hilbert transform on the real line and the discrete Hilbert transform on the integers have the same p–norms. The latter has been a longstanding open problem for many years. Similar problems for other discrete Calderón-Zygmund singular integrals motivate the construction for d greater than 1.
This talk is based on work with Mateusz Kwasnicki (2018) of Wrocław University and Daesung Kim of University of Illinois at Urbana Champaign & Mateusz Kwasnicki (2022)
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