Harmonic Analysis on Spaces of Homogeneous Type [electronic resource] / by Donggao Deng, Yongsheng Han.

Calde?on-Zygmund Operator on Space of Homogeneous Type -- The Boundedness of Calderón-Zygmund Operators on Wavelet Spaces -- Wavelet Expansions on Spaces of Homogeneous Type -- Wavelets and Spaces of Functions and Distributions -- Littlewood-Paley Analysis on Non Homogeneous Spaces.

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.