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Lipschitz spaces via commutators of singular integrals on stratified Lie groups

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posted on 2025-01-22, 02:01 authored by Xuejing Huo

In this thesis, we establish characterisations of Lipschitz spaces on a stratified Lie group G using commutators of Riesz transforms and commutators of fractional integrals. We obtain several equivalence relationships between Lipschitz spaces [formula] and the boundedness of these commutators from Lp(G) spaces (1 < p < ∞) into Triebel–Lizorkin spaces [formula], and from Lp(G) spaces into Lq(G) spaces with suitable conditions on the indices depending on the singular integrals. Moreover, we give a characterisation of BMO spaces on stratified Lie groups using commutators of fractional integrals.

Our results extend the characterisations from the Euclidean setting to the stratified Lie group G. The proofs that overcome the barrier of using Fourier transforms offer new approaches for studying other problems related to the boundedness of operators on stratified Lie groups.

History

Table of Contents

1 Introduction -- 2 Stratified Lie groups and function spaces -- 3 Lipschitz spaces via commutators of Riesz transforms -- 4 Lipschitz spaces via commutators of fractional integrals -- 5 Further study -- References

Awarding Institution

Macquarie University

Degree Type

Thesis MRes

Degree

Master of Research

Department, Centre or School

School of Mathematical and Physical Sciences

Year of Award

2024

Principal Supervisor

Ji Li

Additional Supervisor 1

The Bui

Rights

Copyright: The Author Copyright disclaimer: https://www.mq.edu.au/copyright-disclaimer

Language

English

Extent

95 pages

Former Identifiers

AMIS ID: 379764

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