Radial multipliers and restriction to surfaces of the Fourier transform in mixed-norm spaces

In this article we revisit some classical conjectures in harmonic analysis in the setting of mixed norm spaces L r a d p L a n g 2 R n . We produce sharp bounds for the restriction of the Fourier transform to compact hypersurfaces of revolution in the mixed norm setting and study an extension of the...

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Bibliographic Details
Published in:Mathematische Zeitschrift 2017-08, Vol.286 (3-4), p.1479-1493
Main Authors: Córdoba, Antonio, Latorre Crespo, Eric
Format: Article
Language:English
Subjects:
Fourier analysis
Fourier transforms
Geometry
Harmonic analysis
Mathematics
Mathematics and Statistics
Multipliers
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Summary:In this article we revisit some classical conjectures in harmonic analysis in the setting of mixed norm spaces L r a d p L a n g 2 R n . We produce sharp bounds for the restriction of the Fourier transform to compact hypersurfaces of revolution in the mixed norm setting and study an extension of the disc multiplier. We also present some results for the discrete restriction conjecture and state an intriguing open problem.
ISSN:0025-5874
1432-1823
DOI:10.1007/s00209-016-1810-y