Publication Date

Summer 8-11-2021

Abstract

Linear operators are of huge importance in modern harmonic analysis. Many operators can be dominated by finitely many sparse operators. The main result in this thesis is showing a toy operator, namely the Martingale Transform is dominated by a single sparse operator. Sparse operators are based on a sparse family which is simply a subset of a dyadic grid. We also show the A2 conjecture for the Martingale Transform which follows from the sparse domination of the Martingale Transform and the A2 conjecture for sparse operators.

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Degree Name

Mathematics

Level of Degree

Masters

Department Name

Mathematics & Statistics

First Committee Member (Chair)

Maria Cristina Pereyra

Second Committee Member

Matthew D. Blair

Third Committee Member

Irina Holmes

Language

English

Keywords

Martingale Transform, Sparse Domination, Harmonic Analysis, Hilbert Transform, Dyadic, Calderon Zygmund

Document Type

Thesis

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