15 papers · 1 filter
Quasilinear equations with exponential growth for Hörmander -sub-Laplacians on stratified Lie groups
Jesus A. León Tordecilla, Duván Cardona
We prove the existence of positive weak solutions for a quasilinear equation with exponential nonlinearity on arbitrary stratified Lie groups for \emph{horizontal -Laplacians,}…
Local smoothing estimates for bilinear Fourier integral operators
Duván Cardona
We formulate a local smoothing conjecture for bilinear Fourier integral operators in every dimension derived from the celebrated linear case due to Sogge, which we refer…
Kernel estimates and weak (1,1)-boundedness of pseudo-differential operators on compact Lie groups
Duván Cardona, Rafik Yeghoyan, Michael Ruzhansky
Given a compact Lie group and its unitary dual , we establish the weak (1,1) continuity for pseudo-differential operators in the global Hörmander classes of order…
Boundedness of Fourier Integral Operators with complex phases on Fourier Lebesgue spaces
Duván Cardona, William Obeng-Denteh, Frederick Opoku
In this paper, we develop boundedness estimates for Fourier integral operators on Fourier Lebesgue spaces when the associated canonical relation is parametrised by a complex phase…
The weak (1,1) boundedness of Fourier integral operators with complex phases
Duván Cardona, Michael Ruzhansky
Let be a Fourier integral operator of order associated with a canonical relation locally parametrised by a real-phase function. A fundamental result due to Seeger, S…
Hyperbolic partial differential equations with complex characteristics on Fourier Lebesgue spaces
Duván Cardona, William Obeng-Denteh, Frederick Opoku
The aim of this paper is to establish well-posedness properties for hyperbolic PDEs on Fourier Lebesgue spaces. We consider hyperbolic operators with complex characteristics. Since…