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Singular integrals along variable codimension one subspaces

https://doi.org/10.15781/md28-ws10

Bakas, Odysseas; Di_Plinio, Francesco; Parissis, Ioannis; Roncal, Luz (January 2024, Ars inveniendi analytica)

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Maximal subspace averages

https://doi.org/10.1016/j.aim.2022.108749

Di Plinio, Francesco; Parissis, Ioannis (December 2022, Advances in Mathematics)

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Directional square functions

https://doi.org/10.2140/apde.2023.16.1651

Accomazzo, Natalia; Di_Plinio, Francesco; Hagelstein, Paul; Parissis, Ioannis; Roncal, Luz (January 2023, Analysis & PDE)

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Maximal directional operators along algebraic varieties

https://doi.org/10.1353/ajm.2021.0037

Plinio, Francesco Di; Parissis, Ioannis (January 2021, American Journal of Mathematics)

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Singular integrals along lacunary directions in $R^{n}$

https://doi.org/10.1016/j.aim.2021.107580

Accomazzo, Natalia; Di Plinio, Francesco; Parissis, Ioannis (March 2021, Advances in Mathematics)
null (Ed.)
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On the Maximal Directional Hilbert Transform in Three Dimensions

https://doi.org/10.1093/imrn/rny138

Di Plinio, Francesco; Parissis, Ioannis (June 2018, International Mathematics Research Notices)

Abstract We establish the sharp growth rate, in terms of cardinality, of the $L^p$ norms of the maximal Hilbert transform $$H_\Omega $$ along finite subsets of a finite order lacunary set of directions $$\Omega \subset \mathbb{R}^3$$, answering a question of Parcet and Rogers in dimension $n=3$. Our result is the first sharp estimate for maximal directional singular integrals in dimensions greater than 2. The proof relies on a representation of the maximal directional Hilbert transform in terms of a model maximal operator associated to compositions of 2D angular multipliers, as well as on the usage of weighted norm inequalities, and their extrapolation, in the directional setting.
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