Mathematics and Statistics Faculty and Staff Publications

Document Type

Article

Publication Date

Summer 7-14-2021

Abstract

Linear operators are of huge importance in modern harmonic analysis. Many operators can be dominated by finitely many sparse operators [5]. The main result in this thesis is showing a toy operator, namely the Martingale Transform is dominated by a single sparse operator [6]. Sparse operators are based on a sparse family which is simply a subset of a dyadic grid. We also show the $A_2$ conjecture for the Martingale Transform which follows from the sparse domination of the Martingale Transform and the $A_2$ conjecture for sparse operators [3].

Publisher

UNM Repository

Publication Title

UNM Repository

Keywords

Martingale Transform, Sparse Operator, Calderon Zygmund, Hilbert Transform, Linear Operator, Harmonic Analysis, Dyadic

Included in

Mathematics Commons

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