Francesco Di Plinio

activity

20102026

most citedA sparse domination principle for rough singular integrals

112 citations · 378 across the 30 of their papers we have counts for

collaborators

Showing math.CAShow all

27 papers · 1 filter

math.CA2026

Maximal directional singular integrals

Francesco Di Plinio, Ioannis Parissis

We survey maximal directional averages and directional singular integrals, and their connections with Kakeya--Nikodym phenomena, differentiation theory and the Carleson operator. T…

math.CA2024

Multilinear paraproducts on Sobolev spaces

Francesco Di Plinio, A. Walton Green, Brett D. Wick

Paraproducts are a special subclass of the multilinear Calderón-Zygmund operators, and their Lebesgue space estimates in the full multilinear range are characterized by the $\mathr…

math.CA2023

Pointwise localization and sharp weighted bounds for Rubio de Francia square functions

Francesco Di Plinio, Mikel Flórez-Amatriain, Ioannis Parissis +1

Let $H_{ω} f$ be the Fourier restriction of $f \in L^{2} (R)$ to an interval $ω \subset R$ . If $Ω$ is an arbitrary collection of pairwise disjoint intervals, the square f…

math.CA2023

Wavelet resolution and Sobolev regularity of Calderón-Zygmund operators on domains

Francesco Di Plinio, A. Walton Green, Brett D. Wick

Given a uniform domain $Ω \subset R^{d}$ , we resolve each element of a suitably defined class of Calderòn-Zygmund (CZ) singular integrals on $Ω$ as the linear combination of…

math.CA2022

Singular integrals along variable codimension one subspaces

Odysseas Bakas, Francesco Di Plinio, Ioannis Parissis +1

This article deals with maximal operators on $R^{n}$ formed by taking arbitrary rotations of tensor products of a $d$ -dimensional Hörmander--Mihlin multiplier with the iden…

math.CA2021★ 1 cited

Maximal subspace averages

Francesco Di Plinio, Ioannis Parissis

We study maximal operators associated to singular averages along finite subsets $Σ$ of the Grassmannian $Gr (d, n)$ of $d$ -dimensional subspaces of $R^{n}$ . The well s…

math.CA2021

Bilinear Wavelet Representation of Calderón-Zygmund Forms

Francesco Di Plinio, A. Walton Green, Brett D. Wick

We represent a bilinear Calderón-Zygmund operator at a given smoothness level as a finite sum of cancellative, complexity zero operators, involving smooth wavelet forms, and contin…

math.CA2020★ 1 cited

Wavelet Representation of Singular Integral Operators

Francesco Di Plinio, Brett D. Wick, Tyler Williams

This article develops a novel approach to the representation of singular integral operators of Calderón-Zygmund type in terms of continuous model operators, in both the classical a…

math.CA2020★ 12 cited

A metric approach to sparse domination

José M. Conde Alonso, Francesco Di Plinio, Ioannis Parissis +1

We present a general approach to sparse domination based on single-scale $L^{p}$ -improving as a key property. The results are formulated in the setting of metric spaces of homogeneou…

math.CA2020★ 3 cited

Directional square functions

Natalia Accomazzo, Francesco Di Plinio, Paul Hagelstein +2

Quantitative formulations of Fefferman's counterexample for the ball multiplier are naturally linked to square function estimates for conical and directional multipliers. In this a…

math.CA2019★ 2 cited

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

Natalia Accomazzo, Francesco Di Plinio, Ioannis Parissis

A recent result by Parcet and Rogers is that finite order lacunarity characterizes the boundedness of the maximal averaging operator associated to an infinite set of directions in…

math.CA2018★ 10 cited

Maximal directional operators along algebraic varieties

Francesco Di Plinio, Ioannis Parissis

We establish the sharp growth order, up to epsilon losses, of the $L^{2}$ -norm of the maximal directional averaging operator along a finite subset $V$ of a polynomial variety of arbi…

math.CA2017★ 9 cited

On the maximal directional Hilbert transform in three dimensions

Francesco Di Plinio, Ioannis Parissis

We establish the sharp growth rate, in terms of cardinality, of the $L^{p}$ norms of the maximal Hilbert transform $H_{Ω}$ along finite subsets of a finite order lacunary set of direct…

math.CA2017★ 22 cited

Square functions for bi-Lipschitz maps and directional operators

Francesco Di Plinio, Shaoming Guo, Christoph Thiele +1

First we prove a Littlewood-Paley diagonalization result for bi-Lipschitz perturbations of the identity map on the real line. This result entails a number of corollaries for the Hi…

math.CA2017★ 9 cited

A sharp estimate for the Hilbert transform along finite order lacunary sets of directions

Francesco Di Plinio, Ioannis Parissis

Let $D$ be a nonnegative integer and $Θ \subset S^{1}$ be a lacunary set of directions of order $D$ . We show that the $L^{p}$ norms, $1 < p < \infty$ , of the maximal directional Hi…

math.CA2016★ 112 cited

A sparse domination principle for rough singular integrals

Jose M. Conde-Alonso, Amalia Culiuc, Francesco Di Plinio +1

We prove that bilinear forms associated to the rough homogeneous singular integrals $T_{Ω}$ on $R^{d}$ , where the angular part $Ω \in L^{q} (S^{d - 1})$ has vanishing average and $1…

math.CA2016

Positive sparse domination of variational Carleson operators

Francesco Di Plinio, Yen Q. Do, Gennady N. Uraltsev

Due to its nonlocal nature, the $r$ -variation norm Carleson operator $C_{r}$ does not yield to the sparse domination techniques of Lerner, Di Plinio and Lerner, Lacey. We overcome th…

math.CA2016★ 8 cited

Uniform sparse domination of singular integrals via dyadic shifts

Amalia Culiuc, Francesco Di Plinio, Yumeng Ou

Using the Calderón-Zygmund decomposition, we give a novel and simple proof that $L^{2}$ bounded dyadic shifts admit a domination by positive sparse forms with linear growth in the co…

math.CA2016★ 44 cited

Domination of multilinear singular integrals by positive sparse forms

Amalia Culiuc, Francesco Di Plinio, Yumeng Ou

We establish a uniform domination of the family of trilinear multiplier forms with singularity over a one-dimensional subspace by positive sparse forms involving $L^{p}$ -averages. Th…

math.CA2015★ 2 cited

A modulation invariant Carleson embedding theorem outside local $L^{2}$

Francesco Di Plinio, Yumeng Ou

The article arXiv:1309.0945 by Do and Thiele develops a theory of Carleson embeddings in outer $L^{p}$ spaces for the wave packet transform of functions in $L^{p} (R)$ , in the…

math.CA2015★ 9 cited

Banach-valued multilinear singular integrals

Francesco Di Plinio, Yumeng Ou

We develop a general framework for the analysis of operator-valued multilinear multipliers acting on Banach-valued functions. Our main result is a Coifman-Meyer type theorem for op…

math.CA2014

Endpoint bounds for the bilinear Hilbert transform

Francesco Di Plinio, Christoph Thiele

We study the behavior of the bilinear Hilbert transform $BHT$ at the boundary of the known boundedness region $H$ . A sample of our results is the estimate $| \lan…

math.CA2013★ 38 cited

On weighted norm inequalities for the Carleson and Walsh-Carleson operators

Francesco Di Plinio, Andrei K. Lerner

We prove $L^{p} (w)$ bounds for the Carleson operator $C$ , its lacunary version $C_{l a c}$ , and its analogue for the Walsh series $\W$ in terms of the $A_{q}$ constan…

math.CA2013★ 8 cited

Weak-L^p bounds for the Carleson and Walsh-Carleson operators

Francesco Di Plinio

We prove a weak- $L^{p}$ bound for the Walsh-Carleson operator for $p$ near 1, improving on a theorem of Sjolin. We relate our result to the conjectures that the Walsh-Fourier and Fo…

Maximal directional singular integrals

Multilinear paraproducts on Sobolev spaces

Pointwise localization and sharp weighted bounds for Rubio de Francia square functions

Wavelet resolution and Sobolev regularity of Calderón-Zygmund operators on domains

Singular integrals along variable codimension one subspaces

Maximal subspace averages

Bilinear Wavelet Representation of Calderón-Zygmund Forms

Wavelet Representation of Singular Integral Operators

A metric approach to sparse domination

Directional square functions

Singular integrals along lacunary directions in Rn

Maximal directional operators along algebraic varieties

On the maximal directional Hilbert transform in three dimensions

Square functions for bi-Lipschitz maps and directional operators

A sharp estimate for the Hilbert transform along finite order lacunary sets of directions

A sparse domination principle for rough singular integrals

Positive sparse domination of variational Carleson operators

Uniform sparse domination of singular integrals via dyadic shifts

Domination of multilinear singular integrals by positive sparse forms

A modulation invariant Carleson embedding theorem outside local L2

Banach-valued multilinear singular integrals

Endpoint bounds for the bilinear Hilbert transform

On weighted norm inequalities for the Carleson and Walsh-Carleson operators

Weak-L^p bounds for the Carleson and Walsh-Carleson operators

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

A modulation invariant Carleson embedding theorem outside local $L^{2}$