## 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

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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/bdq127Pierce, 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