Uniform sparse domination and quantitative weighted boundedness for singular integrals and application to the dissipative quasi-geostrophic equation

Yanping Chen, Zihua Guo

Research output: Contribution to journalArticleResearchpeer-review

Abstract

In this paper, we consider a kind of singular integrals [Formula presented] for any f∈Lq(Rn),1<q<∞ and 0<λ<n, which appear in the generalized 2D dissipative quasi-geostrophic (QG) equation ∂tθ+u⋅∇θ+κΛθ=0,(x,t)∈R2×R+,κ>0, where u=−∇Λ−2+2αθ, [Formula presented] and β∈(0,1]. Firstly, we give a uniform sparse domination for this kind of singular integral operators. Secondly, we obtain the uniform quantitative weighted bounds for the operator Tλ with rough kernel. As an application, we obtain the uniform quantitative weighted bounds for the commutator [b,Tλ] with rough kernel and study solutions to the generalized 2D dissipative quasi-geostrophic (QG) equation.

Original languageEnglish
Pages (from-to)871-917
Number of pages47
JournalJournal of Differential Equations
Volume378
DOIs
Publication statusPublished - 5 Jan 2024

Keywords

  • Commutator
  • Generalized 2D dissipative quasi-geostrophic equation
  • Quantitative weighted boundedness
  • Singular integral
  • Sparse domination

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