Maximal Functions, Littlewood-paley Theory, Riesz Transforms and Atomic Decomposition in the Multi-parameter Flag Setting (Memoirs of the American Mathematical Society, 279)

Science & Math

Han, Yongsheng

Li, Ji

Lee, Ming-Yi

Wick, Brett

Mathematics

Amer Mathematical Society

<p>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.</p>

Harmonic Analysis on Spaces of Homogeneous Type (Lecture Notes in Mathematics, 1966)

Deng, Donggao

Springer

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