location:  Publications → journals → CMB
Abstract view

# Estimates for Compositions of Maximal Operators with Singular Integrals

Published:2012-07-27
Printed: Dec 2013
• Richard Oberlin,
Mathematics Department, Louisiana State University, Baton Rouge, LA
 Format: LaTeX MathJax PDF

## Abstract

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 - Multipliers