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We study the continuity in weighted Fourier Lebesgue spaces for a class of pseudodifferential operators, whose symbol has finite Fourier Lebesgue regularity with respect to $x$ and satisfies a quasi-homogeneous decay of derivatives with respect to the $xi$ variable. Applications to Fourier Lebesgue microlocal regularity of linear and nonlinear partial differential equations are given.
We consider nonlinear Schr{o}dinger equations in Fourier-Lebesgue and modulation spaces involving negative regularity. The equations are posed on the whole space, and involve a smooth power nonlinearity. We prove two types of norm inflation results.
In this paper, we study the one-dimensional cubic nonlinear Schrodinger equation (NLS) on the circle. In particular, we develop a normal form approach to study NLS in almost critical Fourier-Lebesgue spaces. By applying an infinite iteration of norma
We prove the existence of ground state solutions for a class of nonlinear elliptic equations, arising in the production of standing wave solutions to an associated family of nonlinear Schrodinger equations. We examine two constrained minimization pro
We develop a second-microlocal calculus of pseudodifferential operators in the semiclassical setting. These operators test for Lagrangian regularity of semiclassical families of distributions on a manifold $X$ with respect to a Lagrangian submanifold
We study the nonlinear Schrodinger equation with initial data in $mathcal{Z}^s_p(mathbb{R}^d)=dot{H}^s(mathbb{R}^d)cap L^p(mathbb{R}^d)$, where $0<s<min{d/2,1}$ and $2<p<2d/(d-2s)$. After showing that the linear Schrodinger group is well-defined in t