5 papers · 1 filter
Regularity and pointwise convergence for dispersive equations on Riemannian symmetric spaces of compact type
Utsav Dewan, Sanjoy Pusti
In this article, we first prove that for general dispersive equations on Riemannian symmetric spaces of compact type , of rank and , the Sobolev regularity t…
Regularity and pointwise convergence for dispersive equations on
Utsav Dewan
In the prototypical setting of non-Euclidean geometry, the 2-dimensional Real Hyperbolic space , we consider the Carleson's problem for the Schrödinger equation and i…
Regularity and pointwise convergence for dispersive equations with asymptotically concave phase on Damek-Ricci spaces
Utsav Dewan
We study the Carleson's problem on Damek-Ricci spaces for dispersive equations: \begin{equation*} \begin{cases} i\frac{\partial u}{\partial t} +Ψ(\sqrt{-\mathcal{L}} )u=0\:,\:…
Iterated convolution inequalities on and Riemannian Symmetric Spaces of non-compact type
Utsav Dewan
In a recent work (Int Math Res Not 24:18604-18612, 2021), Carlen-Jauslin-Lieb-Loss studied the convolution inequality on and proved that the real integra…
Maximal estimates and pointwise convergence for solutions of certain dispersive equations with radial initial data on Damek-Ricci spaces
Utsav Dewan
One of the most celebrated problems in Euclidean Harmonic analysis is the Carleson's problem: determining the optimal regularity of the initial condition of the Schrödinger equ…