相关论文: Fundamental Results for Pseudo-Differential Operat…
This is a continuation of recent work on the general definition of pseudo-differential operators of type $1,1$, in H\"ormander's sense. Continuity in $L_p$-Sobolev spaces and H\"older--Zygmund spaces, and more generally in Besov and…
This dissertation concerns the pseudo-differential operators of type 1,1. These have been known especially since around 1980, when it was shown that they play an important role in the treatment of fully non-linear partial differential…
The main result is that every pseudo-differential operator of type 1,1 and order $d$ is continuous from the Triebel--Lizorkin space $F^d_{p,1}$ to $L_p$, $1\le p<\infty$, and that this is optimal within the Besov and Triebel--Lizorkin…
Pseudo-differential operators of type $(1,1)$ and order $m$ are continuous from $F_p^{s+m,q}$ to $F_p^{s,q}$ if $s>d/\min{(1,p,q)}-d$ for $0<p<\infty$, and from $B_p^{s+m,q}$ to $B_{p}^{s,q}$ if $s>d/\min{(1,p)}-d$ for $0<p\leq\infty$. In…
This paper presents a general definition of pseudo-differential operators of type $1,1$; the definition is shown to be the largest one that is both compatible with negligible operators and stable under vanishing frequency modulation.…
Pseudo-differential operators of type 1,1 are proved continuous from the Triebel--Lizorkin space $F^d_{p,1}$ to $L_p$ for $1\le p<\infty$, when of order d, and this is the largest possible domain among the Besov and Triebel--Lizorkin…
Given a compact Lie group $G$ and its unitary dual $\widehat{G}$, we establish the weak (1,1) continuity for pseudo-differential operators in the global H\"ormander classes of order $-n(1-\rho)/2$ on $G\times \widehat{G}$. Our approach…
We define a class of discrete operators acting on infinite, finite or periodic sequences mimicking the standard properties of pseudo-differential operators. In particular we can define the notion of order and regularity, and we recover the…
In this article, we conduct a study of integral operators defined in terms of non-convolution type kernels with singularities of various degrees. The operators that fall within our scope of research include fractional integrals, fractional…
In this paper we obtain the weak type (1,1) boundedness of Calderon-Zygmund operators acting over operator-valued functions. Our main tools for its solution are a noncommutative form of Calderon-Zygmund decomposition in conjunction with a…
Related to a semigroup of operators on a metric measure space, we define and study pseudodifferential operators (including the setting of Riemannian manifold, fractals, graphs ...). Boundedness on $L^p$ for pseudodifferential operators of…
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…
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,…
A study of diff($S^1$) covariant properties of pseudodifferential operator of integer degree is presented. First, it is shown that the action of diff($S^1$) defines a hamiltonian flow defined by the second Gelfand-Dickey bracket if and only…
A fundamental result in pseudodifferential theory is the Calder\'on-Vaillancourt theorem, which states that a pseudodifferential operator defined from a H\"ormander symbol of order $0$ defines a bounded operator on $L^2(\mathbb{R}^d)$. In…
The purpose of this paper is to introduce new definitions of H\"ormander classes for pseudo-differential operators over the compact group of $p$-adic integers. Our definitions possess a symbolic calculus, asymptotic expansions and…
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,…
Specific global symbol classes and corresponding pseudodifferential operators of infinite order that act continuously on the space of tempered ultradistributions of Beurling and Roumieu type are constructed. For these classes, symbolic…
Consider an h-pseudodifferential operator P, whose symbol extends holomorphically to a tubular neighborhood of the real phase space and converges sufficiently fast to 1, so that the determinant of P is well-defined. We show that the modulus…
In this paper we continue our program of revisiting the new aspects about the boundedness properties of pseudo-differential operators on the torus. Here we prove $H^p$-$L^p$ and $H^p$-estimates for H\"ormander classes of pseudo-differential…