Related papers: Micro-local analysis in Fourier Lebesgue and modul…

Let $\omega ,\omega_0$ be appropriate weight functions and $q\in [1,\infty ]$. We introduce the wave-front set, $\WF_{\mathscr FL^q_{(\omega)}}(f)$ of $f\in \mathscr S'$ with respect to weighted Fourier Lebesgue space $\mathscr…

We consider multiplication properties of elements in weighted Fourier Lebesgue and modulation spaces. Especially we extend some results by Pilipovic, Teofanov and Toft (2010).

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…

Some results of microlocal continuity for pseudodifferential operators whose non regular symbols belong to weighted Fourier Lebesgue spaces are given. Inhomogeneous local and microlocal propagation of singularities of Fourier Lebesgue type…

This paper focuses on the study of semilinear fractional diffusion-wave equations in the context of critical nonlinearities. Firstly, we address the issue of local well-posedness for the problem, examine spatial regularity, and the…

We obtain discrete characterizations of wave front sets of Fourier-Lebesgue and quasianalytic type. It is shown that the microlocal properties of an ultradistribution can be obtained by sampling the Fourier transforms of its localizations…

We define and study wave-front sets for weighted Fourier-Lebesgue spaces when the weights are moderate with respect to the associated functions for general sequences $\{ M_p\} $ which satisfy Komatsu's conditions $(M.1) - (M.3)'$. In…

We prove a sharp higher differentiability result for local minimizers of functionals of the form $$\mathcal{F}\left(w,\Omega\right)=\int_{\Omega}\left[ F\left(x,Dw(x)\right)-f(x)\cdot w(x)\right]dx$$ with non-autonomous integrand $F(x,\xi)$…

The local well-posedness problem is considered for the Dirac-Klein-Gordon system in two space dimensions for data in Fourier-Lebesgue spaces $\hat{H}^{s,r}$ , where $\|f\|_{\hat{H}^{s,r}} = \| \langle \xi \rangle^s \hat{f}\|_{L^{r'}}$ and…

We connect through the Fourier transform shift-invariant Sobolev type spaces $V_s\subset H^s$, $s\in\mathbb R,$ and the spaces of periodic distributions and analyze the properties of elements in such spaces with respect to the product. If…

We prove some local (in time) wellposedness results for nonlinear Schroedinger equations with rough data, that is, the initial value belongs to some Sobolev space of negative index. The proof uses the Fourier restriction norm method.

We prove local well-posedness for the periodic derivative nonlinear Schrodinger's equation, which is L^2 critical, in Fourier-Lebesgue spaces which scale like H^s(T) for s>0. In particular we close the existing gap in the subcritical theory…

In this paper, we investigate the existence of weak solution for a fractional type problems driven by a nonlocal operator of elliptic type in a fractional Orlicz-Sobolev space, with homogeneous Dirichlet boundary conditions. We first extend…

We consider the Cauchy problem for an equation of the form \partial_t+\partial_x^3)u=F(u,u_x,u_{xx}) where F is a polynomial with no constant or linear terms and no quadratic uu_{xx} term. For a polynomial nonlinearity with no quadratic…

Let $G$ be a compact Lie group. In this article, we consider the initial value fractional wave equation with power-type nonlinearity on $G$. Mainly, we investigate some $L^{2}-L^{2}$ estimates of the solutions to the homogeneous fractional…

In this paper we extend some results from our earlier papers on wave-front sets, concerning wave-front sets of Fourier-Lebesgue and modulation space types, to a broader class of spaces of ultradistributions, and relate these wave-front sets…

Given the Fourier-Legendre expansions of $f$ and $g$, and mild conditions on $f$ and $g$, we derive the Fourier-Legendre expansion of their product in terms of their corresponding Fourier-Legendre coefficients. In this way, expansions of…

This paper is dedicated to the study of the semilinear fractional diffusion-wave equation. We provide estimates on the families of linear operators related to the problem in the fractional power scale associated with the Laplace operator.…

Given a bilinear (or sub-bilinear) operator $B$, we prove restricted weighted weak type inequalities of the form $$ ||B(f_1, f_2)||_{L^{p, \infty}(w_1^{p/p_1}w_2^{p/p_2})}\lesssim ||f_1||_{L^{p_1, 1}(w_1)}||f_2||_{L^{p_2, 1}(w_2)}, $$…

Let $\Omega \subset \mathbb{R}^N$, $N \geq 2$, be a smooth bounded domain. For $s \in (1/2,1)$, we consider a problem of the form \[ \left\{\begin{aligned} (-\Delta)^s u & = \mu(x)\, \mathbb{D}_s^{2}(u) + \lambda f(x)\,, & \quad \mbox{in}…