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Estimates for Compositions of Maximal Operators with Singular Integrals

 Printed: Dec 2013
  • Richard Oberlin,
    Mathematics Department, Louisiana State University, Baton Rouge, LA
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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 maximal operator calderon-zygmund
MSC Classifications: 42A45 show english descriptions Multipliers 42A45 - Multipliers

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