Molecular decomposition of localizable Hardy spaces and applications

The theory of real Hardy spaces, denoted by Hp, and its local version hp, has been extensively developed since the 1960s. Among the countless important properties of these spaces, one can make note the atomic and molecular decomposition, which allows to describe a distribution on this space in terms of particular functions called atoms and molecules. These latter objects represent the basic building blocks of Hardy spaces and it turns out that some important properties of the space itself and operators acting on them can be obtained looking at this particular decomposition, which is plenty easier to handle. Although the molecular theory for Hp is fully developed, for the local version this structure is not completely understood yet. The goal of this project is to investigate and propose the right molecular decomposition for hp and apply it to get the boundedness of some classical operators in Harmonic Analysis, such as strongly singular Calderón-Zygmund operators.

Faculty Supervisor:

Galia Dafni

Student:

Partner:

Universidade de São Paulo

Discipline:

Mathematics

Sector:

Education

University:

Concordia University

Program: