Estimates for Compositions of Maximal Operators with Singular Integrals

http://dx.doi.org/10.4153/CMB-2012-003-x
12 pages

  Published:2012-07-27
 

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.