Publication Date

Fall 12-20-2017

Abstract

A so-called space of homogeneous type is a set equipped with a quasi-metric and a doubling measure. We give a survey of results spanning the last few decades concerning the geometric properties of such spaces, culminating in the description of a system of dyadic cubes in this setting whose properties mirror the more familiar dyadic lattices in R^n . We then use these cubes to prove a result pertaining to weighted inequality theory over such spaces. We develop a general method for extending Bellman function type arguments from the real line to spaces of homogeneous type. Finally, we uses this method to extend some recent results in the theory of weighted dyadic operators.

Degree Name

Mathematics

Level of Degree

Doctoral

Department Name

Mathematics & Statistics

First Committee Member (Chair)

Maria Cristina Pereyra

Second Committee Member

Matthew Blair

Third Committee Member

Ana Skripka

Fourth Committee Member

Maxim Zenchenko

Fifth Committee Member

Lesley Ward

Language

English

Keywords

Harmonic Analysis, Spaces of Homogeneous Type

Document Type

Dissertation

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