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On discrete fractional integral operators and mean values of Weyl sums

Abstract:

In this paper, we prove new ℓp→ℓq bounds for a discrete fractional integral operator by applying techniques motivated by the circle method of Hardy and Littlewood to the Fourier multiplier of the operator. From a different perspective, we describe explicit interactions between the Fourier multiplier and mean values of Weyl sums. These mean values express the average behaviour of the number rs, k(l) of representations of a positive integer l as a sum of s positive kth powers. Recent deep resul...

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Publication status:
Published

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Publisher copy:
10.1112/blms/bdq127

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Institution:
University of Oxford
Department:
Oxford, MPLS, Mathematical Inst
Role:
Author
Journal:
BULLETIN OF THE LONDON MATHEMATICAL SOCIETY
Volume:
43
Issue:
3
Pages:
597-612
Publication date:
2011-06-05
DOI:
EISSN:
1469-2120
ISSN:
0024-6093
URN:
uuid:06141d54-2eb6-4115-88cb-4edbbe31dfbf
Source identifiers:
188063
Local pid:
pubs:188063
Language:
English

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