Multilinear Calderón–zygmund Singular Integrals

This paper contains the material covered in a minicourse given by the author at the Centre de Recerca Matemàtica in Barcelona during the period May 4–9, 2009. The course was an expanded version of a series of three lectures delivered by the author two weeks earlier (April 23–25) at the New Mexico Analysis Seminar held at the University of New Mexico in Albuquerque. The author would like to thank Joan Mateu and Joan Orobitg for coordinating two special minicourses at the Centre de Recerca Matemàtica on Multilinear Harmonic Analysis and Weights presented by the author and Professor Carlos Pérez during the period May 4–8, 2009. These mincourses were part of a special research program for the academic year 2008–2009 entitled Harmonic Analysis, Geometric Measure Theory, and Quasiconformal Mappings, coordinated by Xavier Tolsa and Joan Verdera. The author would also like to thank the Centre de Recerca Matemàtica for providing an inspiring environment for research to the participants during these workshops. This research was partially supported by the NSF under grant DMS 0900946.