On discrete fractional integral operators and mean values of Weyl sums
Publication
, Journal Article
Pierce, LB
Published in: Bulletin of the London Mathematical Society
2011
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 results within the context of Waring's problem and Weyl sums enable us to prove a further range of complementary results for the discrete operator under consideration. © 2011 London Mathematical Society.
Duke Scholars
Published In
Bulletin of the London Mathematical Society
DOI
ISSN
0024-6093
Publication Date
2011
Volume
43
Issue
3
Start / End Page
597 / 612
Related Subject Headings
- General Mathematics
- 4904 Pure mathematics
- 0101 Pure Mathematics
Citation
APA
Chicago
ICMJE
MLA
NLM
Pierce, L. B. (2011). On discrete fractional integral operators and mean values of Weyl sums. Bulletin of the London Mathematical Society, 43(3), 597–612. https://doi.org/10.1112/blms/bdq127
Pierce, L. B. “On discrete fractional integral operators and mean values of Weyl sums.” Bulletin of the London Mathematical Society 43, no. 3 (2011): 597–612. https://doi.org/10.1112/blms/bdq127.
Pierce LB. On discrete fractional integral operators and mean values of Weyl sums. Bulletin of the London Mathematical Society. 2011;43(3):597–612.
Pierce, L. B. “On discrete fractional integral operators and mean values of Weyl sums.” Bulletin of the London Mathematical Society, vol. 43, no. 3, 2011, pp. 597–612. Scival, doi:10.1112/blms/bdq127.
Pierce LB. On discrete fractional integral operators and mean values of Weyl sums. Bulletin of the London Mathematical Society. 2011;43(3):597–612.
Published In
Bulletin of the London Mathematical Society
DOI
ISSN
0024-6093
Publication Date
2011
Volume
43
Issue
3
Start / End Page
597 / 612
Related Subject Headings
- General Mathematics
- 4904 Pure mathematics
- 0101 Pure Mathematics