112 citations · 378 across the 30 of their papers we have counts for
35 papers
Artificial intelligence pathways from weather to climate
Tom Beucler, J. David Neelin, Hui Su +10
Deep learning has made rapid advances in weather forecasting: autoregressive models trained on atmospheric reanalyses now rival dynamical models across nowcasting, medium-range, an…
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…
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…
Quantitative Sobolev regularity of quasiregular maps
Francesco Di Plinio, A. Walton Green, Brett D. Wick
We quantify the Sobolev space norm of the Beltrami resolvent , where is the Beurling-Ahlfors transform, in terms of the corresponding Sobolev s…
Pointwise localization and sharp weighted bounds for Rubio de Francia square functions
Francesco Di Plinio, Mikel Flórez-Amatriain, Ioannis Parissis +1
Let be the Fourier restriction of to an interval . If is an arbitrary collection of pairwise disjoint intervals, the square f…
Wavelet resolution and Sobolev regularity of Calderón-Zygmund operators on domains
Francesco Di Plinio, A. Walton Green, Brett D. Wick
Given a uniform domain , we resolve each element of a suitably defined class of Calderòn-Zygmund (CZ) singular integrals on as the linear combination of…
Singular integrals along variable codimension one subspaces
Odysseas Bakas, Francesco Di Plinio, Ioannis Parissis +1
This article deals with maximal operators on formed by taking arbitrary rotations of tensor products of a -dimensional Hörmander--Mihlin multiplier with the iden…
Maximal subspace averages
Francesco Di Plinio, Ioannis Parissis
We study maximal operators associated to singular averages along finite subsets of the Grassmannian of -dimensional subspaces of . The well s…
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…
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…
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 -improving as a key property. The results are formulated in the setting of metric spaces of homogeneou…
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…
Singular integrals along lacunary directions in
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…
Maximal directional operators along algebraic varieties
Francesco Di Plinio, Ioannis Parissis
We establish the sharp growth order, up to epsilon losses, of the -norm of the maximal directional averaging operator along a finite subset of a polynomial variety of arbi…
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 norms of the maximal Hilbert transform along finite subsets of a finite order lacunary set of direct…
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…
A sharp estimate for the Hilbert transform along finite order lacunary sets of directions
Francesco Di Plinio, Ioannis Parissis
Let be a nonnegative integer and be a lacunary set of directions of order . We show that the norms, , of the maximal directional Hi…
Navier-Stokes-Voigt equations with memory in 3D lacking instantaneous kinematic viscosity
Francesco Di Plinio, Andrea Giorgini, Vittorino Pata +1
We consider a Navier-Stokes-Voigt fluid model where the instantaneous kinematic viscosity has been completely replaced by a memory term incorporating hereditary effects, in presenc…
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 on , where the angular part has vanishing average and $1…
Positive sparse domination of variational Carleson operators
Francesco Di Plinio, Yen Q. Do, Gennady N. Uraltsev
Due to its nonlocal nature, the -variation norm Carleson operator does not yield to the sparse domination techniques of Lerner, Di Plinio and Lerner, Lacey. We overcome th…
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 bounded dyadic shifts admit a domination by positive sparse forms with linear growth in the co…
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 -averages. Th…
A modulation invariant Carleson embedding theorem outside local
Francesco Di Plinio, Yumeng Ou
The article arXiv:1309.0945 by Do and Thiele develops a theory of Carleson embeddings in outer spaces for the wave packet transform of functions in , in the…
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…