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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-zygmundCategory:42A45

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