A Remark on Littlewood-paley Theory for the Distorted Fourier Transform
نویسنده
چکیده
We consider the classical theorems of Mikhlin and LittlewoodPaley from Fourier analysis in the context of the distorted Fourier transform. The latter is defined as the analogue of the usual Fourier transform as that transformation which diagonalizes a Schrödinger operator −∆+ V . We show that for such operators which display a zero energy resonance the full range 1 < p < ∞ in the Mikhlin theorem cannot be obtained: in the radial, threedimensional case it shrinks to 3 2 < p < 3.
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