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arXiv · 1110.1070

Estimates for compositions of maximal operators with singular integrals

Richard Oberlin
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Abstract

We prove weak-type (1,1) estimates for compositions of maximal operators with singular integrals. Our main object of interest is the operator $Δ^*Ψ$ where $Δ^*$ is Bourgain's maximal multiplier operator and $Ψ$ is the sum of several modulated singular integrals; here our method yields a significantly improved bound for the $L^q$ operator norm when $1 < q < 2$. We also consider associated variation-norm estimates.

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Richard Oberlin. 2011-10-05. Estimates for compositions of maximal operators with singular integrals. https://doi.org/10.4153/cmb-2012-003-x

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