Thesis Defense: "Paraproducts and Well Localized Operators"

Abstract: Paraproducts are essential tools in Harmonic Analysis, providing a convenient way to
decompose more complicated operators into discrete objects. In the present work, we provide
results on the composition of paraproducts in both the n dimensional setting as well
as in spaces of homogeneous type. We further explore the properties of a more general class
of operators, well localized operators, which were first introduced by Nazarov, Treil and
Volberg. We give a new characterization of these operators and provide a new proof for the
two weight boundedness of these operators.