Modern Harmonic Analysis is a very active field of theoretical research which plays in a central position within the mathematical sciences. Singular integrals and weighted norm inequalities are core topics of research in Harmonic Analysis.
In many problems one is interested in the continuity properties of linear and/or multilinear operators that have some degree of singularity. Such operators arise naturally in diverse areas of analysis and applications like the regularity properties of partial differential equations as in the case of the solutions of the Beltrami operator where the Beurling transform plays the central role. Moreover, they also appear in multilinear form in the analysis of product type non-linearities involving functions and their derivatives. The general idea is to find understand norm inequalities in various function spaces defined in the Euclidean space or in more general domains to quantify the boundedness properties of such operators.