Geodesic
Estimates for Compositions of Maximal Operators with Singular Integrals
Canadian mathematical bulletin, Tome 56 (2013) no. 4, pp. 801-813

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DOI

We prove weak-type $\left( 1,\,1 \right)$ 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 $1\,<\,q\,<\,2$ . We also consider associated variation-norm estimates.
DOI : 10.4153/CMB-2012-003-x
Mots-clés : 42A45, maximal operator, Calderón–Zygmund 
Oberlin, Richard. Estimates for Compositions of Maximal Operators with Singular Integrals. Canadian mathematical bulletin, Tome 56 (2013) no. 4, pp. 801-813. doi: 10.4153/CMB-2012-003-x
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     author = {Oberlin, Richard},
     title = {Estimates for {Compositions} of {Maximal} {Operators} with {Singular} {Integrals}},
     journal = {Canadian mathematical bulletin},
     pages = {801--813},
     year = {2013},
     volume = {56},
     number = {4},
     doi = {10.4153/CMB-2012-003-x},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2012-003-x/}
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