A remark on Littlewood-Paley theory for the distorted Fourier transform
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Abstract:
We consider the classical theorems of Mikhlin and Littlewood-Paley 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 $-\Delta +V$. We show that for such operators which display a zero energy resonance the full range $1<p< \infty$ in the Mikhlin theorem cannot be obtained: in the radial, three-dimensional case it shrinks to $\frac 32<p<3$.References
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Additional Information
- W. Schlag
- Affiliation: Department of Mathematics, University of Chicago, 5734 South University Ave., Chicago, Illinois 60637
- MR Author ID: 313635
- Email: schlag@math.uchicago.edu
- Received by editor(s): August 29, 2005
- Published electronically: August 4, 2006
- Additional Notes: The author was partially supported by NSF grant DMS-0300081 and a Sloan Fellowship.
- Communicated by: Andreas Seeger
- © Copyright 2006
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 135 (2007), 437-451
- MSC (2000): Primary 35J10, 42B15; Secondary 35P10, 42B25
- DOI: https://doi.org/10.1090/S0002-9939-06-08621-7
- MathSciNet review: 2255290