Estimates for Compositions of Maximal Operators with Singular Integrals

Canadian mathematical bulletin

Richard Oberlin¹ 

[1] Mathematics Department, Louisiana State University, Baton Rouge, LA

关键词: maximal operator calderon-zygmund;   

DOI  :  10.4153/CMB-2012-003-x

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

We prove weak-type $(1,1)$ estimates for compositions of maximaloperators with singular integrals. Our main object of interest is theoperator $Delta^*Psi$ where $Delta^*$ is Bourgain's maximalmultiplier operator and $Psi$ is the sum of several modulatedsingular integrals; here our method yields a significantly improvedbound for the $L^q$ operator norm when $1 lt q lt 2.$ We also considerassociated variation-norm estimates.

【 授权许可】

Unknown