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DISCRETE FRACTIONAL RADON TRANSFORMS AND QUADRATIC FORMS

Abstract:

We consider discrete analogues of fractional Radon transforms involving integration over paraboloids defined by positive definite quadratic forms. We prove sharp results for this class of discrete operators in all dimensions, providing necessary and sufficient conditions for them to extend to bounded operators from l p to l q. The method involves an intricate spectral decomposition according to major and minor arcs, motivated by ideas from the circle method of Hardy and Littlewood. Techniques...

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Publication status:
Published

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Publisher copy:
10.1215/00127094-1507288

Authors


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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Role:
Author
Journal:
DUKE MATHEMATICAL JOURNAL More from this journal
Volume:
161
Issue:
1
Pages:
69-106
Publication date:
2012-01-15
DOI:
ISSN:
0012-7094
Language:
English
Pubs id:
pubs:254525
UUID:
uuid:1dc5dd33-d008-437e-8f82-2538dad5cf47
Local pid:
pubs:254525
Source identifiers:
254525
Deposit date:
2012-12-19

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