- 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...
Expand abstract - Publication status:
- Published
- Publisher copy:
- 10.1112/blms/bdq127
-
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- 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
- Copyright date:
- 2011
Journal article
On discrete fractional integral operators and mean values of Weyl sums
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