The Real and Complex Techniques in Harmonic Analysis from the Point of View of Covariant Transform
arXiv:1209.5072
Abstract
This note reviews complex and real techniques in harmonic analysis. We describe a common source of both approaches rooted in the covariant transform generated by the affine group. Keywords: wavelet, coherent state, covariant transform, reconstruction formula, the affine group, ax+b-group, square integrable representations, admissible vectors, Hardy space, fiducial operator, approximation of the identity, maximal functions, atom, nucleus, atomic decomposition, Cauchy integral, Poisson integral, Hardy--Littlewood maximal functions, grand maximal function, vertical maximal functions, non-tangential maximal functions, intertwining operator, Cauchy-Riemann operator, Laplace operator, singular integral operator, SIO, boundary behaviour, Carleson measure.
31 pages, AMS-LaTeX, no figures; v2: a major revision, sections on representations of the ax+b group and transported norms are added; v3: major revision: an outline section on complex and real variables techniques are added, numerous smaller improvements; v4: minor corrections
References in corpus (2)
Cited by in corpus (5)
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