36 citations · 42 across the 8 of their papers we have counts for
10 papers
Probabilistic well-posedness of generalized cubic nonlinear Schrödinger equations with strong dispersion using higher order expansions
Jean-baptiste Casteras, Juraj Földes, Itamar Oliveira +1
In this paper, we study the local well-posedness of the cubic Schrödinger equation …
Higher order expansion for the probabilistic local well-posedness theory for a cubic nonlinear Schrödinger equation
Jean-Baptiste Casteras, Juraj Foldes, Gennady Uraltsev
In this paper, we study the probabilistic local well-posedness of the cubic Schrödinger equation (cubic NLS): \[ (i\partial_{t} + Δ) u = \pm |u|^{2} u \text{ on } [0,T) \times \mat…
The full range of uniform bounds for the bilinear Hilbert transform
Gennady Uraltsev, Michał Warchalski
We prove uniform uniform bounds for the family of bilinear Hilbert transforms $\mathrm{BHT}_β [f_1, f_2] (x) := \mathrm{p.v.} \int_{\mathbb{R}} f_1 (x - t) f_2 (x + βt) \fr…
Almost sure local well-posedness for cubic nonlinear Schrodinger equation with higher order operators
Jean-Baptiste Casteras, Juraj Foldes, Gennady Uraltsev
In this paper, we study the local well-posedness of the cubic Schrödinger equation: \[ (i \partial_t - \mathscr{L}) u = \pm |u|^2 u \quad \text{ on } I \times \mathbb{R}^d, \] with…
Variational Carleson operators in UMD spaces
Alex Amenta, Gennady Uraltsev
We prove -boundedness of variational Carleson operators for functions valued in intermediate UMD spaces. This provides quantitative information on the rate of convergence of p…
The bilinear Hilbert transform in UMD spaces
Alex Amenta, Gennady Uraltsev
We prove -bounds for the bilinear Hilbert transform acting on functions valued in intermediate UMD spaces. Such bounds were previously unknown for UMD spaces that are not Bana…
Banach-valued modulation invariant Carleson embeddings and outer- spaces: the Walsh case
Alex Amenta, Gennady Uraltsev
We prove modulation invariant embedding bounds from Bochner spaces on the Walsh group to outer- spaces on the Walsh extended phase plane. The Banach space…
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…
Variational Carleson embeddings into the upper 3-space
Gennady Uraltsev
In this paper we formulate embedding maps into time-frequency space related to the Carleson operator and its variational counterpart. We prove bounds for these embedding maps by it…
On the Distributional Hessian of the Distance Function
Carlo Mantegazza, Giovanni Mascellani, Gennady Uraltsev
We describe the precise structure of the distributional Hessian of the distance function from a point of a Riemannian manifold. In doing this we also discuss some geometrical prope…