Interaction between the Fourier transform and the Hilbert transform
Keywords:Fourier transform, Hilbert transform, real Hardy space, atomic decomposition, Hardy's inequality, bounded variation
AbstractWell-known and recently observed situations where the two main transforms in harmonic analysis, the Fourier transform and the Hilbert transform, show their adjacency and interplay in a specic interesting manner are overviewed. Some relations of that kind are new, while in other cases well-known formulas are considered in a different setting.
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