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Estimates for Compositions of Maximal Operators with Singular Integrals

Published online by Cambridge University Press:  20 November 2018

Richard Oberlin
Richard Oberlin*
Affiliation:
Mathematics Department, Louisiana State University, Baton Rouge, LAe-mail: oberlin@math.lsu.edu
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Abstract.

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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.

Keywords

42A45maximal operatorCalderón–Zygmund

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 56 , Issue 4 , 01 December 2013 , pp. 801 - 813
Copyright
Copyright © Canadian Mathematical Society 2013

References

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