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Harmonic Analysis on Spaces of Homogeneous Type

  • Donggao Deng
  • Yongsheng Han

Part of the Lecture Notes in Mathematics book series (LNM, volume 1966)

About this book

Introduction

The dramatic changes that came about in analysis during the twentieth century are truly amazing.
In the thirties, complex methods and Fourier series played a seminal role. After many improvements, mostly achieved by the Calderón-Zygmund school, the action today is taking place in spaces of homogeneous type. No group structure is available and the Fourier transform is missing, but a version of harmonic analysis is still available. Indeed the geometry is conducting the analysis.
The authors succeed in generalizing the construction of wavelet bases to spaces of homogeneous type. However wavelet bases are replaced by frames, which in many applications serve the same purpose.

Keywords

Calderon-Zygmund operator Calderon’s identity Fourier transform Littlewood-Paley analysis T1 theorem Wavelets harmonic analysis

Authors and affiliations

  • Donggao Deng
    • 1
  • Yongsheng Han
    • 1
  1. 1.Department of Mathematics and StatisticsAuburn UniversityAuburnUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-540-88745-4
  • Copyright Information Springer Berlin Heidelberg 2009
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-540-88744-7
  • Online ISBN 978-3-540-88745-4
  • Series Print ISSN 0075-8434
  • Buy this book on publisher's site