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Singular integrals with rough kernals and BMO spaces associated to operators

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posted on 2022-03-28, 21:21 authored by Georges Nader
The purpose of this thesis is to study the new criterion for boundedness of some singular integrals. The main results of this thesis are presented in four parts. --1. Recall the Hörmander condition for boundedness of singular integrals which has been an important result of the Calderón-Zygmund theory. -- 2. Discuss a new criterion for singular integral operators to be bounded on Lp(X), 1< p < ∞ , where X is a space of homogeneous type. This criterion is an improvement of the Hörmander condition and it has had many applications in recent research of singular integrals in the last 20 years. -- 3. Discuss new function spaces which suit these operators such as BMOA spaces associated to operators. -- 4. Use these results to study the functional calculus of operators satisfying certain kernel estimates.


Table of Contents

1 Introduction -- 2 Calderón-Zygmund Theory and BMO(Rn) -- 3 Singular Integrals with Rough Kernels -- 4 Spaces BMOA Associated with the Generalized Approximation to the Identity -- 5 Applications: Holomorphic Functional Calculus of Elliptic Operators


Theoretical thesis. Bibliography page 49

Awarding Institution

Macquarie University

Degree Type

Thesis MRes


MRes, Macquarie University, Faculty of Science, Department of Mathematics and Statistics

Department, Centre or School

Department of Mathematics and Statistics

Year of Award


Principal Supervisor

Xuan Thinh Duong


Copyright 2020




1 online resource (49 pages)

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