77 citations · 191 across the 52 of their papers we have counts for
60 papers
On the boundedness for the bilinear quadratic functional given by arbitrary strips
Frédéric Bernicot
This study provides initial results on the boundedness of the (smooth) bilinear quadratic functional defined by an arbitrary collection of disjoint strips. The square function unde…
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^{…
Biparameter under the action of a rotation
Frédéric Bernicot, Yujia Zhai
In this work, we aim to study the action of composing by a rotation on the biparameter space in . This space is not preserved by a rotation…
Boundedness of some multi-parameter fiber-wise multiplier operators
Frédéric Bernicot, Polona Durcik
We prove estimates for various multi-parameter bi- and trilinear operators with symbols acting on fibers of the two-dimensional functions. In particular, this yields estimate…
A bilinear Rubio de Francia inequality for arbitrary rectangles
Frédéric Bernicot, Marco Vitturi
Let be a collection of disjoint dyadic rectangles with sides parallel to the axes, let denote the non-smooth bilinear projection onto \[ π_R (f,g)(x):=\…
Bilinear Rubio de Francia inequalities for collections of non-smooth squares
Frédéric Bernicot, Marco Vitturi
Let be a collection of disjoint dyadic squares , let denote the non-smooth bilinear projection onto \[ π_ω(f,g)(x):=\int\int \mathbf{1}_ω(ξ,η) \widehat{f}(ξ) \wide…