Estimates for Compositions of Maximal Operators with Singular Integrals

Abstract

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 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.