A remark on Littlewood-Paley theory for the distorted Fourier transform

Details A remark on Littlewood-Paley theory for the distorted Fourier transform A remark on Littlewood-Paley theory for the distorted Fourier transform

2005-08-29

arxiv.org/abs/math/0508577v1

Mathematics

Classical Analysis and ODEs

Scientific paper

We show that the usual Mikhlin multiplier theorem relative to the distorted Fourier transform holds in the range (3/2,3) at least for radial functions and potentials. The restricted range is due to the fact that the Schroedinger operator which gives rise to the distorted Fourier transform may have a zero energy resonance. Consequently, the Littlewood-Paley theorem is shown also only for the range (3/2,3).

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