相关论文: Micro-local analysis in Fourier Lebesgue and modul…
In this paper we study the boundedness in weighted variable Lebesgue spaces of operators associated with the semigroup generated by the time-independent Schr\"odinger operator $\mathcal{L}=-\Delta+V$ in $\mathbb{R}^d$, where $d>2$ and the…
Fourier integral operators with sufficiently smooth phase act on the time-frequency content of functions. However time-frequency analysis has only recently been used to analyze these operators. In this paper, we show that if a Fourier…
Last years there was increasing an interest to the so called function spaces with non-standard growth, known also as variable exponent Lebesgue spaces. For weighted such spaces on homogeneous spaces, we develop a certain variant of Rubio de…
Let $(X, d, \mu)$ be a space of homogeneous type and $\Omega$ an open subset of $X$. Given a bounded operator $T: L^p(\Omega) \to L^q(\Omega)$ for some $1 \le p \le q < \infty$, we give a criterion for $T$ to be of weak type $(p_0, a)$ for…
We consider local modifications $\omega_n+f^*\omega_d$ of the Fubini-Study metric (with associated $(1,1)$-form $\omega_n$) on an open subset $\Omega\subset \bC\bP^n$ induced by a local holomorphic mapping $f\colon \Omega\to \bP^d$. Our…
We completely characterize the spectrum of a weighted composition operator $W_{\psi, \varphi}$ on $H^{2}(\mathbb{D})$ when $\varphi$ has Denjoy-Wolff point $a$ with $0<|\varphi '(a)|< 1$, the iterates, $\varphi_{n}$, converge uniformly to…
In this work we characterise the H\"ormander classes $\symbClassOn{m}{\rho}{\delta}{\group,\textnormal{H\"or}}$ on the open manifold $\group = (-1,1)^n$. We show that by endowing the open manifold $\group = (-1,1)^n$ with a group structure,…
Fractional Sobolev spaces $\widehat{H}^s(\mathbb{R})$ have been playing important roles in analysis of many mathematical subjects. In this work, we re-consider fractional Sobolev spaces under the perspective of fractional operators and…
Following the work of Duistermaat-Singer \cite{DS} on isomorphisms of algebras of global pseudodifferential operators, we classify isomorphisms of algebras of microlocally defined semiclassical pseudodifferential operators. Specifically, we…
In the paper we extend the spectral invariance of pseudodifferential operators acting on (non-weighted) classical modulation spaces to allow the Lebesgue exponents to be smaller than one. These spaces occur naturally in approximation theory…
We consider Fourier integral operators with symbols in modulation spaces and non-smooth phase functions whose second orders of derivatives belong to certain types of modulation space. We establish continuity and Schatten-von Neumann…
Let $A_{1},...A_{m}$ be a $n\times n$ invertible matrices. Let $0 \leq \alpha<n$ and $0<\alpha_{i}<n$ such that $\alpha_1 + ... + \alpha_m = n- \alpha$. We define% \begin{equation*} T_{\alpha}f(x)=\int \frac{1}{\left\vert…
Previously, spectra of certain weighted composition operators on the Hardy Space were discovered under one of two hypotheses: either the compositional symbol converges under iteration to the Denjoy-Wolff point on all of the open disk rather…
In this paper, we study harmonic analysis on the affine Poincar\'e group $\mathcal{P}_{aff}$, which is a non-unimodular group, and obtain pseudo-differential operators with operator valued symbols. More precisely, we study the boundedness…
The essential support of the symbol of a semiclassical pseudodifferentail operator is characterized by semiclassical wavefront sets of distributions. The proof employs a coherent state whose center in phase space is dependent on Planck's…
Neural operators have shown great potential in solving a family of Partial Differential Equations (PDEs) by modeling the mappings between input and output functions. Fourier Neural Operator (FNO) implements global convolutions via…
The sharp Wolff-type decoupling estimates of Bourgain--Demeter are extended to the variable coefficient setting. These results are applied to obtain new sharp local smoothing estimates for wave equations on compact Riemannian manifolds,…
In this paper we obtain new estimates for bilinear pseudodifferential operators with symbol in the class $BS_{1,1}^m$, when both arguments belong to Triebel-Lizorkin spaces of the type $F_{p,q}^{n/p}(\mathbb{R}^n)$. The inequalities are…
Let $s\ge 1$, $\omega ,\omega_0\in \mathscr P_{E,s}^0$, $a\in \Gamma _{s}^{(\omega_0)}$, and let $\mathscr B$ be a suitable invariant quasi-Banach function space, Then we prove that the pseudo-differential operator $\operatorname{Op} (a)$…
We develop a semiclassical second microlocal calculus of pseudodifferential operators associated to linear coisotropic submanifolds $\mathcal{C}\subset T^* \mathbb{T}^n$, where $\mathbb{T}^n = \mathbb{R}^n / \mathbb{Z}^n$. First…