56 citations · 88 across the 11 of their papers we have counts for
11 papers
The oscillatory biest operator
Cristina Benea, Itamar Oliveira
We prove the boundedness of a trilinear operator that is modulation invariant and which contains curvature information given by the presence of a complex exponential, adding to the…
Multi-parameter flag Leibniz rules of arbitrary complexity in mixed-norm spaces
Cristina Benea, Yujia Zhai
We prove multi-parameter Leibniz rules corresponding to flag paraproducts of arbitrary complexity in mixed-norm spaces, including endpoint estimates. The proof relies on multi-line…
The non-resonant bilinear Hilbert--Carleson operator
Cristina Benea, Frederic Bernicot, Victor Lie +1
In this paper we introduce the class of bilinear Hilbert--Carleson operators defined by $$ BC^{a}(f,g)(x):= \sup_{λ\in {\mathbb R}} \Big|\int f(x-t)\, g(x+t)\, e^{…
Mixed-norm estimates via the helicoidal method
Cristina Benea, Camil Muscalu
We prove multiple vector-valued and mixed-norm estimates for multilinear operators in $\rr R^d$, more precisely for multilinear operators associated to a symbol singular alon…
Multiple vector-valued, mixed norm estimates for Littlewood-Paley square functions
Cristina Benea, Camil Muscalu
We prove that for any -valued Schwartz function defined on , one has the multiple vector-valued, mixed norm estimate $$ \| f \|_{L^P(L^Q)} \lesssim \| S f \|…
The Helicoidal Method
Cristina Benea, Camil Muscalu
This is an expository paper on the helicoidal method, a tool designed for proving multiple vector-valued inequalities for operators in harmonic analysis, which is based on stopping…
Sparse domination via the helicoidal method
Cristina Benea, Camil Muscalu
Using exclusively the localized estimates upon which the helicoidal method was built, we show how sparse estimates can also be obtained. This approach yields a sparse domination fo…
Quasi-Banach Valued Inequalities via the Helicoidal method
Cristina Benea, Camil Muscalu
We extend the helicoidal method that we previously developed to the quasi-Banach context, proving in this way multiple Banach and quasi-Banach vector-valued inequalities for parapr…
Sparse bilinear forms for Bochner Riesz multipliers and applications
Cristina Benea, Frederic Bernicot, Teresa Luque
We use the very recent approach developed by Lacey in [23] and extended by Bernicot-Frey-Petermichl in [3], in order to control Bochner-Riesz operators by a sparse bilinear form. I…
A bilinear Rubio de Francia inequality for arbitrary squares
Cristina Benea, Frederic Bernicot
We prove the boundedness of a smooth bilinear Rubio de Francia operator associated with an arbitrary collection of squares (with sides parallel to the axes) in the frequency plane\…
Multiple Vector Valued Inequalities via the Helicoidal Method
Cristina Benea, Camil Muscalu
We develop a new method of proving vector-valued estimates in harmonic analysis, which we like to call "the helicoidal method". As a consequence of it, we are able to give affirmat…