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1. CMB 2012 (vol 56 pp. 801)

Oberlin, Richard
Estimates for Compositions of Maximal Operators with Singular Integrals
We prove weak-type $(1,1)$ estimates for compositions of maximal operators with singular integrals. Our main object of interest is the operator $\Delta^*\Psi$ where $\Delta^*$ is Bourgain's maximal multiplier operator and $\Psi$ is the sum of several modulated singular integrals; here our method yields a significantly improved bound for the $L^q$ operator norm when $1 \lt q \lt 2.$ We also consider associated variation-norm estimates.

Keywords:maximal operator calderon-zygmund

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