Multilinear theory of strongly singular Calderón-Zygmund operators and applications
type: Item
instance of: scholarly article
title: Multilinear theory of strongly singular Calderón-Zygmund operators and applications
zbMATH Open document ID: 1439.42021
author: Yan Lin
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2020-04-07T00:00:00Z
review text: The main purpose of this paper is to study the multilinear strongly singular Calderón-Zygmund operators whose kernels are more singular near the diagonal than that of the standard multilinear Calderón-Zygmund operator. The sharp maximal pointwise estimate for the multilinear strongly singular Calderón-Zygmund operator is established. As applications, the boundedness of the multilinear strongly singular Calderón-Zygmund operator on the product of weighted Lebesgue spaces and on the product of variable exponent Lebesgue spaces is obtained respectively. Moreover, three kind of endpoint estimates of the types $L^{\infty} \times \cdots \times L^{\infty} \rightarrow BMO$, $BMO \times \cdots \times BMO \rightarrow BMO$, and $LMO \times \cdots \times LMO \rightarrow LMO$ are established for the multilinear strongly singular Calderón-Zygmund operator. These results improve the corresponding known ones for the standard multilinear Calderón-Zygmund operators.
Mathematics Subject Classification ID: 42B20
Mathematics Subject Classification ID: 42B35
Mathematics Subject Classification ID: 42B25
zbMATH DE Number: 7187804
zbMATH Keywords: multilinear strongly singular Calderón-Zygmund operator
zbMATH Keywords: sharp maximal function
zbMATH Keywords: BMO function
zbMATH Keywords: LMO function
zbMATH Keywords: singular integral
zbMATH Keywords: weighted Lebesgue space
zbMATH Keywords: variable exponent Lebesgue space
reviewed by: Koichi Saka
MaRDI profile type: Publication
full work available at URL: j.na.2019.111699
OpenAlex ID: W2991270903
cites work: On \(BMO\) regularity for linear elliptic systems
cites work: \(H^ p\) continuity properties of Calderón-Zygmund-type operators
cites work: Vector valued inequalities for strongly singular Calderón-Zygmund operators
cites work: Global \(W^{1,p(\cdot)}\) estimate for renormalized solutions of quasilinear equations with measure data on Reifenberg domains
cites work: Weighted norm inequalities for multilinear operators and applications to multilinear Fourier multipliers
cites work: Weighted Norm Inequalities for Strongly Singular Convolution Operators
cites work: On Commutators of Singular Integrals and Bilinear Singular Integrals
cites work: Q3941791
cites work: Commutateurs d'intégrales singulières et opérateurs multilinéaires
cites work: Variable Lebesgue spaces. Foundations and harmonic analysis
cites work: Q5291662
cites work: Maximal functions on Musielak--Orlicz spaces and generalized Lebesgue spaces
cites work: Lebesgue and Sobolev spaces with variable exponents
cites work: Calderón-Zygmund operators on generalized Lebesgue spaces Lp(⋅) and problems related to fluid dynamics
cites work: Inequalities for strongly singular convolution operators
cites work: \(H^p\) spaces of several variables
cites work: Q3700300
cites work: Extrapolation of weighted norm inequalities for multivariable operators and applications
cites work: Maximal operator and weighted norm inequalities for multilinear singular integrals
cites work: Multilinear Calderón-Zygmund theory
cites work: Bilinear square functions and vector-valued Calderón-Zygmund operators
cites work: A new proof of the bilinear T(1) Theorem
cites work: On multiplier transformations
cites work: A note on multilinear fractional integrals
cites work: Multilinear estimates and fractional integration
cites work: Q4021390
cites work: New maximal functions and multiple weights for the multilinear Calderón-Zygmund theory
cites work: Weak and strong type weighted estimates for multilinear Calderón-Zygmund operators
cites work: Strongly singular Calderón-Zygmund operator and commutator on Morrey type spaces
cites work: Weighted Lipschitz estimates for commutators on weighted Morrey spaces
cites work: Toeplitz operators related to strongly singular Calderón--Zygmund operators
cites work: Boundedness of commutators on Hardy-type spaces
cites work: Strongly singular Calderón-Zygmund operators and their commutators
cites work: Strongly singular Calderón-Zygmund operators and commutators on weighted Morrey spaces
cites work: Multilinear Calderón-Zygmund operators with kernels of Dini's type and applications
cites work: Weighted norm inequalities for paraproducts and bilinear pseudodifferential operators with mild regularity
cites work: Weighted inequalities for multilinear fractional integral operators
cites work: Q4462261
cites work: Minimal regularity conditions for the end-point estimate of bilinear Calderón-Zygmund operators
cites work: Partial Differential Equations with Variable Exponents
cites work: Q5597805
cites work: Q5567326
cites work: Q3142876
cites work: An Endpoint estimate for the commutator of singular integrals
cites work: Special trigonometric series in 𝑘-dimensions
cites work: Well/ill-posedness for the dissipative Navier-Stokes system in generalized Carleson measure spaces
DOI: 10.1016/J.NA.2019.111699
description: scientific article; zbMATH DE number 7187804