Revista Matemática Iberoamericana

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Volume 23, Issue 2, 2007, pp. 705–742
DOI: 10.4171/RMI/510

Published online: 2007-08-31

Paraproducts with flag singularities I. A case study

Camil Muscalu[1]

(1) Cornell University, Ithaca, USA

In this paper we prove $L^p$ estimates for a tri-linear operator, whose symbol is given by the product of two standard symbols, satisfying the well known Marcinkiewicz-Hörmander-Mihlin condition. Our main result contains in particular the classical Coifman-Meyer theorem. This tri-linear operator is the simplest example of a large class of multi-linear operators, which we called \textit{paraproducts with flag singularities}.

Keywords: paraproducts, $L^{1,\infty}$-sizes, $L^{1,\infty}$-energies, flag singularities

Muscalu Camil: Paraproducts with flag singularities I. A case study. Rev. Mat. Iberoamericana 23 (2007), 705-742. doi: 10.4171/RMI/510