This paper is concerned with the Cauchy problem of the 2D Zakharov-Kuznetsov equation.
We prove bilinear estimates which imply local in time well-posedness in the Sobolev space …

We prove local in time well-posedness for the Zakharov system in two space dimensions
with large initial data in L 2× H− 1/2× H− 3/2. This is the space of optimal regularity in the …

Uniform L 2-estimates for the convolution of singular measures with respect to transversal
submanifolds are proved in arbitrary space dimension. The results of Bennett–Bez are used …

147 A short proof of the multilinear Kakeya inequality Page 1 Math. Proc. Camb. Phil. Soc. (2015),
158, 147–153 c Cambridge Philosophical Society 2014 doi:10.1017/S0305004114000589 …

We prove that the best constant in the general Brascamp-Lieb inequality is a locally
bounded function of the underlying linear transformations. As applications we deduce …

We prove a nonlinear variant of the general Brascamp–Lieb inequality. Our proof consists of
running an efficient, or “tight,” induction-on-scales argument, which uses the existence of …

The purpose of this article is to survey certain aspects of multilinear harmonic analysis
related to notions of transversality. Particular emphasis will be placed on the multilinear …

The Zakharov-Kuznetsov equation in space dimension $ d\geq 3$ is considered. It is proved
that the Cauchy problem is locally well-posed in $ H^ s (\mathbb {R}^ d) $ in the full …

In this paper, we establish local well-posedness for the Zakharov system on T d, d≥ 3 in a
low regularity setting. Our result improves the work of Kishimoto (J Anal Math 119: 213–253 …

Firstly, bilinear Fourier restriction estimates—which are well known for free waves—are
extended to adapted spaces of functions of bounded quadratic variation, under quantitative …