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Discrete Multilinear Spherical Averages

Part of: Harmonic analysis in several variables Exponential sums and character sums

Published online by Cambridge University Press:  09 January 2019

Brian Cook
Brian Cook*
Affiliation:
Department of Mathematical Sciences, Kent State University, Kent, Ohio, USA Email: briancookmath@gmail.com
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Abstract

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In this note we give a characterization of $\ell ^{p}\times \cdots \times \ell ^{p}\rightarrow \ell ^{q}$ boundedness of maximal operators associated with multilinear convolution averages over spheres in $\mathbb{Z}^{n}$.

Keywords

discrete maximal functionmultilinear average

MSC classification

Primary: 11L07: Estimates on exponential sums
Secondary: 42B25: Maximal functions, Littlewood-Paley theory
Type
Article
Information
Canadian Mathematical Bulletin , Volume 62 , Issue 2 , June 2019 , pp. 243 - 246
Copyright
© Canadian Mathematical Society 2018 

Footnotes

The author was supported in part by NSF grant DMS1147523.

References

Bourgain, J., On 𝛬(p)-subsets of squares . Israel J. Math. 67(1989), no. 3, 291–311. https://doi.org/10.1007/BF02764948.Google Scholar
Henriot, K. and Hughes, K., Discrete restriction estimates of 𝜀-removal type for kth-powers and k-paraboloids . Math. Ann., to appear.Google Scholar
Magyar, Á., Stein, E., and Wainger, S., Discrete analogues in harmonic analysis: spherical averages . Ann. of Math. 155(2002), 189–208. https://doi.org/10.2307/3062154.Google Scholar
Oberlin, D. M., A multilinear Young’s inequality . Canad. Math. Bull. 31(1988), no. 3, 380–384. https://doi.org/10.4153/CMB-1988-054-0.Google Scholar
Oberlin, D. M., Multilinear convolutions defined by measures on spheres . Trans. Amer. Math. Soc. 310(1988), no. 2, 821–835. https://doi.org/10.1090/S0002-9947-1988-0943305-7.Google Scholar
Wooley, T., Discrete Fourier restriction via efficient congruencing . Int. Math. Res. Not.(2017), no. 5, 1342–1389. https://doi.org/10.1093/imrn/rnw031.Google Scholar