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Speaker: Luz Roncal (BCAM - Basque Center for Applied Mathematics, Spain)
Title: Pointwise localisation and weighted inequalities for Rubio de Francia square function
Abstract:
Let us denote by Rubio de Francia square function the square function formed by frequency projections on a collection of disjoint intervals of the real line. J. L. Rubio de Francia established in 1985 that this operator is bounded on L^p for p≥2 and on L^p(w), for p greater than 2, with weights w in the Muckenhoupt class A_p/2. What happens in the endpoint L^1(w) for w∈A_1 was left open, and Rubio de Francia conjectured the validity of the estimate in this endpoint.
In this talk we will show a new pointwise sparse estimate for the Rubio de Francia square function. Such a bound implies quantitative weighted estimates which, in some cases, improve the available results. We will also confirm that the L^2(w) conjecture is verified for radially decreasing even A_1 weights, and in full generality for the Walsh group analogue to the Rubio de Francia square function. In general, the L^2 weighted inequality is still an open problem.
Joint work with Francesco Di Plinio, Mikel Flórez-Amatriain, and Ioannis Parissis.
Негізгі бет APRG Seminar: 2024-04-10 - Luz Roncal
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