An extension of Calderón-Zygmund type singular integral with non-smooth kernel
type: Item
instance of: scholarly article
title: An extension of Calderón-Zygmund type singular integral with non-smooth kernel
zbMATH Open document ID: 1479.42035
author: Yanyan Li
published in: Journal of Functional Analysis
publication date: 2021-09-14T00:00:00Z
review text: In this article the authors studied the following singular integral \[Tf(x)=\mathrm{p.v.}\int_{\mathbb{R}^n}\frac{\Omega(y)}{|y|^{n-\beta}}f(x-y)dy,\] where \(f\in L^1(\mathbb{R}^n)\cap L^q(\mathbb{R}^n)\), \(1\leq q<\infty\) and \(0<\beta<n\). This type of singular integral can be viewed as an extension of the classical Calderón-Zygmund type singular integral. Moreover, this kind of singular integral appears in the approximation of the surface quasi-geostrophic equation from the generalized surface quasi-geostrophic equation. The authors established an estimate of the singular integral in the \(L^q\) space for \(1<q<\infty\) and a weak \((1,1)\) type of the singular integral when \(0<\beta<(q-1)n\) and \(\Omega\in L^\infty(\mathrm{S}^{n-1})\). Particularly, the bounds do not depend on \(\beta\). Personally speaking, this paper is very interesting and very well written. This paper involves a large amount of definitions, notation and references, which increases its richness. Meanwhile, these elements also add a lot of difficulty. Overall, this article is a very nice piece of work.
reviewed by: Feng Liu
Mathematics Subject Classification ID: 42B20
Mathematics Subject Classification ID: 42B37
Mathematics Subject Classification ID: 35Q35
zbMATH DE Number: 7395042
zbMATH Keywords: Calderón-Zygmund singular
zbMATH Keywords: non-smooth kernel
MaRDI profile type: Publication
full work available at URL: j.jfa.2021.109196
OpenAlex ID: W3185865862
cites work: Infinite time aggregation for the critical Patlak‐Keller‐Segel model in ℝ2
cites work: Critical mass for a Patlak-Keller-Segel model with degenerate diffusion in higher dimensions
cites work: Q4389910
cites work: On the existence of certain singular integrals
cites work: Formation of strong fronts in the 2-D quasigeostrophic thermal active scalar
cites work: Maximal and singular integral operators via Fourier transform estimates
cites work: Finite time singularity for the modified SQG patch equation
cites work: Local Regularity for the Modified SQG Patch Equation
cites work: A new proof for the estimates of Calderón-Zygmund type singular integrals
cites work: Q3199050
cites work: Singular integral operators with rough convolution kernels
cites work: Q5607484
cites work: A geometric approach to the Calderón-Zygmund estimates
cites work: An extension of Riesz transform
cites work: Remarks on well-posedness of the generalized surface quasi-geostrophic equation
cites work: An extension of Calderón-Zygmund type singular integral
DOI: 10.1016/J.JFA.2021.109196
Recommended article: An extension of Calderón-Zygmund type singular integral
Recommended article: A new proof for the estimates of Calderón-Zygmund type singular integrals
Recommended article: CALDERÓN-ZYGMUND THEORY FOR KERNELS WITH NONDISCRETE SETS OF SINGULARITIES
Recommended article: Q3362818
Recommended article: On multilinear singular integrals of Calderón-Zygmund type
Recommended article: A new approach to \(L^{p}\) estimates for Calderón-Zygmund type singular integrals
Recommended article: Calderon-Zygmund singular integral estimates in generalized weighted function spaces
Recommended article: Q4224825
Recommended article: Multilinear oscillatory integrals with Calderón-Zygmund kernel
Recommended article: A note on Calderón-Zygmund singular integral convolution operators
description: scientific article; zbMATH DE number 7395042