The weighted \(L^ p\)-boundedness of product-type pseudodifferential operators
type: Item
instance of: scholarly article
title: The weighted \(L^ p\)-boundedness of product-type pseudodifferential operators
zbMATH Open document ID: 0676.35090
DOI: 10.1016/0001-8708(89)90003-0
author: Masao Yamazaki
published in: Advances in Mathematics
publication date: 1989-01-01T00:00:00Z
review text: The author considers non-regular simple and double symbols satisfying estimates of \(S^ 0_{1,\delta}\)-type, and gives new conditions on the smoothness of the symbols, which are sufficient for the unweighted \(L^ p\)-boundedness of the associated pseudodifferential operators. The above conditions are shown to be sufficient for the boundedness on \(L^ r(w)\), where \(r\geq p\) and w is an \(A^{r/p}\)-weight of Muckenhoupt, thus filling the gap between the sufficient conditions for the unweighted \(L^ p\)-boundedness and those for the weighted \(L^ p\)-boundedness. These results are generalized to pseudodifferential operators on product domains. The proof uses paradifferential operators, the maximal inequality, and the estimate of the kernels.
Mathematics Subject Classification ID: 35S05
Mathematics Subject Classification ID: 35B35
Mathematics Subject Classification ID: 35B65
Mathematics Subject Classification ID: 46E30
zbMATH DE Number: 4107326
zbMATH Keywords: non-regular simple and double symbols
zbMATH Keywords: estimates
zbMATH Keywords: smoothness
zbMATH Keywords: unweighted \(L^ p\)-boundedness
zbMATH Keywords: \(A^{r/p}\)-weight of Muckenhoupt
zbMATH Keywords: product domains
zbMATH Keywords: paradifferential operators
zbMATH Keywords: maximal inequality
reviewed by: Rémi Vaillancourt
MaRDI profile type: Publication
full work available at URL: 0001-8708(89)90003-0
OpenAlex ID: W2063979501
cites work: Weighted inequalities for vector-valued maximal functions and singular integrals
cites work: Lp-Estimates for certain non-regular eudo-differential operators.
cites work: Some recent developments in Fourier analysis and 𝐻^{𝑝}-theory on product domains
cites work: Sharp function and weighted \(L^ p\) estimates for a class of pseudo- differential operators
cites work: Q3941791
cites work: Calderón-Zygmund theory for product domains: H p spaces
cites work: Singular integrals on product spaces
cites work: Calderon-Zygmund operators, pseudo-differential operators and the Cauchy integral of Calderon
cites work: Calderón-Zygmund operators on product spaces
cites work: Q4178004
cites work: Weighted Sobolev Spaces and Pseudodifferential Operators with Smooth Symbols
cites work: Estimates for Pseudo-Differential Operators of Class S0,0
cites work: Lp-boundedness of pseudo-differential operators with non-regular symbols
cites work: Q4141616
cites work: Q3779145
cites work: On sufficient conditions for the boundedness of pseudo-differential operators
cites work: The Lp-boundedness of pseudo-differential operators with non-regular symbols
cites work: Q3331670
cites work: Q3769336
cites work: Weighted norm inequalities for certain pseudo-differential operators
cites work: Q3812826
cites work: Generalizations of Calderón-Zygmund operators
cites work: Calderón-zygmund operators and pseudo-differential operators
cites work: Weighted norm inequalities for pseudo-differential operators
cites work: The \(L^ p\)-boundedness of pseudo-differential operators satisfying estimates of parabolic type and product type. II
cites work: The \(L^ p\)-boundedness of pseudodifferential operators with estimates of parabolic type and product type
description: scientific article; zbMATH DE number 4107326