Nonregular pseudo-differential operators
type: Item
instance of: scholarly article
title: Nonregular pseudo-differential operators
zbMATH Open document ID: 0840.47040
DOI: 10.4171/ZAA/691
author: Yanyan Li
published in: Zeitschrift für Analysis und ihre Anwendungen
publication date: 1996-03-17T00:00:00Z
review text: Summary: We study the boundedness properties of pseudo-differential operators \(a(x, D)\) and their adjoints \(a(x, D)^*\) with symbols in a certain vector-valued Besov space on Besov spaces \(B^s_{p, q}\) and Triebel spaces \(F^s_{p, q}\) \((0< p, q\leq \infty)\). Applications are given to multiplication properties of Besov and Triebel spaces. We show that our results are best possible for both pseudo-differential estimates and multiplication. Denoting by \((\cdot,\cdot)\) the duality between Besov and between Triebel spaces we derive general conditions under which \((a(x, D) f, g)= (f, a(x, D)^*g)\) holds. This requires a precise definition of \(a(x, D)f\) and \(a(x, D)^*f\) for \(f\in F^s_{p, q}\) and \(f\in B^s_{p, q}\).
Mathematics Subject Classification ID: 47G30
Mathematics Subject Classification ID: 46E35
Mathematics Subject Classification ID: 35S50
zbMATH DE Number: 856809
zbMATH Keywords: nonregular symbols
zbMATH Keywords: paramultiplication
zbMATH Keywords: pointwise multiplication
zbMATH Keywords: boundedness
zbMATH Keywords: pseudo-differential operators
zbMATH Keywords: vector-valued Besov space
zbMATH Keywords: multiplication properties of Besov and Triebel spaces
MaRDI profile type: Publication
cites work: On the Spaces of T<scp>riebel‐</scp>L<scp>izorkin</scp> Type: Pointwise Multipliers and Spaces on Domains
cites work: A discrete transform and decompositions of distribution spaces
cites work: Pointwise Multiplication of Besov and Triebel‐Lizorkin Spaces
cites work: Some remarks on Triebel spaces
cites work: Pseudo-Differential Operators with Coefficients in Sobolev Spaces
cites work: Weighted Parabolic Triebel Spaces of Product Type. Fourier Multipliers and Pseudo-Differential Operators
cites work: Microlocal Analysis for Solutions of Nonlinear Partial Differential Equations in Weighted Function Spaces
cites work: Parametrices for Nonregular Elliptic Pseudodifferential Operators
cites work: On the Boundedness and Compactness of Nonregular Pseudo‐Differential Operators
cites work: Q3927555
cites work: Q3810339
cites work: Pointwise multiplication in Triebel-Lizorkin spaces
cites work: Hölder inequalities and sharp embeddings in function spaces of \(B_{pq}^ s\) and \(F_{pq}^ s\) type
cites work: Pseudodifferential operators and nonlinear PDE
cites work: Q5557339
cites work: Q4195422
cites work: Q3336200
cites work: Q4003552
cites work: Q3808742
full work available at URL: https://doi.org/10.4171/zaa/691
OpenAlex ID: W2078583296
description: scientific article; zbMATH DE number 856809