Related papers: Weighted periodic and discrete Pseudo-Differential…

In this paper, we introduce and study a class of pseudo-differential operators on the lattice $\mathbb{Z}^n$. More preciously, we consider a weighted symbol class $M_{\rho, \Lambda}^m(\mathbb{ Z}^n\times \mathbb{T}^n), m\in \mathbb{R}$…

In this article, we introduce and study $M$-elliptic pseudo-differential operators in the framework of non-harmonic analysis of boundary value problems on a manifold $\Omega$ with boundary $\partial \Omega$, introduced by Ruzhansky and…

In this paper, we study the $M$-ellipticity of Fredholm pseudo-differential operators associated with weighted symbols on $L^p(\mathbb{R}^n)$, $1 < p < \infty$. We also prove the G\r{a}rding's inequality for $M$-elliptic operators and the…

The purpose of this paper is to prove pointwise inequalities and to establish the boundedness on weighted $L^{p}$ spaces for pseudo-differential operators $T_{a}$ defined by the symbol $a\in S^{m}_{\varrho,\delta}$ with $0\leq\varrho\leq1,$…

In this paper we develop the calculus of pseudo-differential operators on the lattice $\mathbb{Z}^n$, which we can call pseudo-difference operators. An interesting feature of this calculus is that the phase space is compact so the symbol…

We prove a symbolic calculus for a class of pseudodifferential operators, and discuss its applications to $L^2$-compactness via a compact version of the $T(1)$ theorem.

We establish general weighted $L^2$ inequalities for pseudodifferential operators associated to the H\"ormander symbol classes $S^m_{\rho,\delta}$. Such inequalities allow to control these operators by fractional "non-tangential" maximal…

In this paper we consider the semiclassical version of pseudo-differential operators on the lattice space $\hbar \mathbb{Z}^n$. The current work is an extension of a previous work and agrees with it in the limit of the parameter $\hbar…

We obtain weighted $L^p$ inequalities for pseudo-differential operators with smooth symbols and their commutators by using a class of new weight functions which include Muckenhoupt weight functions. Our results improve essentially some…

This paper finishes the goal of the authors started in two previous manuscripts dedicated to revisiting the continuity properties of toroidal pseudo-differential operators with symbols in the H\"ormander classes. Here we prove pointwise…

We consider two types of multilinear pseudodifferential operators. First, we prove the boundedness of multilinear pseudodifferential operators with symbols which are only measurable in the spatial variables in weighted Lebesgue spaces.…

We establish a H\"{o}rmander type theorem for the multilinear pseudo-differential operators, which is also a generalization of the results in \cite{MR4322619} to symbols depending on the spatial variable. Most known results for multilinear…

We construct a Weyl pseudodifferential calculus tailored to studying boundedness of operators on weighted $L^p$ spaces over $\mathbb{R}^d$ with weights of the form $\exp(-\phi(x))$, for $\phi$ a $C^2$ function, a setting in which the…

We extend the matrix representation of magnetic pseudo-differential operators in a tight Gabor frame from [arXiv:1804.05220, arXiv:2212.12229] to asymmetrical quantizations and smooth symbols dominated by a tempered weight (and not just…

In this paper, we study the boundedness of pseudodifferential operators with symbols in the H\"ormander class $S^0_{\rho,\rho}$ on $\alpha$-modulation spaces $M_{p,q}^{s,\alpha}$, and consider the relation between $\alpha$ and $\rho$. In…

In this paper we prove $L^p$-estimates for H\"ormander classes of pseudo-differential operators on the torus $\mathbb{T}^n$. The results are presented in the context of the global symbolic calculus of Ruzhansky and Turunen on…

In this monograph we develop magnetic pseudodifferential theory for operator-valued and equivariant operator-valued functions and distributions from first principles. These have found plentiful applications in mathematical physics,…

Consider an elliptic self-adjoint pseudodifferential operator $A$ acting on $m$-columns of half-densities on a closed manifold $M$, whose principal symbol is assumed to have simple eigenvalues. We show existence and uniqueness of $m$…

In previous papers, a generalization of the Weyl calculus was introduced in connection with the quantization of a particle moving in $\mathbb R^n$ under the influence of a variable magnetic field $B$. It incorporates phase factors defined…

For operators belonging either to a class of global bisingular pseudodifferential operators on $R^m \times R^n$ or to a class of bisingular pseudodifferential operators on a product $M \times N$ of two closed smooth manifolds, we show the…