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Weighted and endpoint estimates for commutators of bilinear pseudo-differential operators

AIMS Mathematics, 2022
In this paper, by applying the accurate estimates of the Hörmander class, the authors consider the commutators of bilinear pseudo-differential operators and the operation of multiplication by a Lipschitz function.
Yanqi Yang, Shuangping Tao, Guanghui Lu
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Computation of Pseudo-Differential Operators [PDF]

SIAM Journal on Scientific Computing, 1996
Summary: A simple algorithm is described for computing general pseudo-differential operator actions. Our approach is based on the asymptotic expansion of the symbol together with the fast Fourier transform. The idea is motivated by the characterization of the pseudo-differential operator algebra.
Bao, Gang, Symes, William W.
openaire +2 more sources

Pseudo-differential operators and equations in a discrete half-space

Mathematical Modelling and Analysis, 2018
We introduce a digital pseudo-differential operator acting in discrete Sobolev--Slobodetskii spaces and consider pseudo-differential equations with such operators in a discrete half-space.
Alexander V. Vasilyev, Vladimir B. Vasilyev +1 more
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Pseudo-differential operators in algebras of generalized functions and global hypoellipticity [PDF]

, 2004
The aim of this work is to develop a global calculus for pseudo-differential operators acting on suitable algebras of generalized functions. In particular, a condition of global hypoellipticity of the symbols gives a result of regularity for the ...
Garetto, Claudia
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Branching Asymptotics on Manifolds with Edge [PDF]

, 2010
We study pseudo-differential operators on a wedge with continuous and variable discrete branching asymptotics.Comment: 54 pages, 1 ...
Schulze, B. -Wolfgang, Volpato, Andrea
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Fundamental Results for Pseudo-Differential Operators of Type 1, 1

Axioms, 2016
This paper develops some deeper consequences of an extended definition, proposed previously by the author, of pseudo-differential operators that are of type 1 , 1 in Hörmander’s sense. Thus, it contributes to the long-standing problem of creating
Jon Johnsen
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Hormander class of pseudo-differential operators on compact Lie groups and global hypoellipticity [PDF]

, 2010
In this paper we give several global characterisations of the Hormander class of pseudo-differential operators on compact Lie groups. The result is applied to give criteria for the ellipticity and the global hypoellipticity of pseudo-differential ...
A Bergamasco +19 more
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Towards semi-classical analysis for sub-elliptic operators

Bruno Pini Mathematical Analysis Seminar, 2022
We discuss the recent developments of semi-classical and micro-local analysis in the context of nilpotent Lie groups and for sub-elliptic operators.
Véronique Fischer
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Kadomtsev-Petviashvili hierarchies with non-formal pseudo-differential operators, non-formal solutions, and a Yang-Mills–like formulation

Physics Letters B
We start from the classical Kadomtsev-Petviashvili (KP) hierarchy posed on formal pseudo-differential operators, and we produce new hierarchies of non-linear equations in the context of non-formal pseudo-differential operators lying in the Kontsevich and
Jean-Pierre Magnot, Enrique G. Reyes
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$L^p$-boundedness and $L^p$-nuclearity of multilinear pseudo-differential operators on $\mathbb{Z}^n$ and the torus $\mathbb{T}^n$

, 2019
In this article, we begin a systematic study of the boundedness and the nuclearity properties of multilinear periodic pseudo-differential operators and multilinear discrete pseudo-differential operators on $L^p$-spaces. First, we prove analogues of known
Cardona, Duván, Kumar, Vishvesh
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pseudodifferential operators
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