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Discrete Multilinear Spherical Averages

  • Brian Cook (a1)
Abstract

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 $\mathbb{Z}^{n}$ .

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The author was supported in part by NSF grant DMS1147523.

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[1] Bourgain, J., On 𝛬(p)-subsets of squares . Israel J. Math. 67(1989), no. 3, 291311. https://doi.org/10.1007/BF02764948.
[2] Henriot, K. and Hughes, K., Discrete restriction estimates of 𝜀-removal type for kth-powers and k-paraboloids . Math. Ann., to appear.
[3] Magyar, Á., Stein, E., and Wainger, S., Discrete analogues in harmonic analysis: spherical averages . Ann. of Math. 155(2002), 189208. https://doi.org/10.2307/3062154.
[4] Oberlin, D. M., A multilinear Young’s inequality . Canad. Math. Bull. 31(1988), no. 3, 380384. https://doi.org/10.4153/CMB-1988-054-0.
[5] Oberlin, D. M., Multilinear convolutions defined by measures on spheres . Trans. Amer. Math. Soc. 310(1988), no. 2, 821835. https://doi.org/10.1090/S0002-9947-1988-0943305-7.
[6] Wooley, T., Discrete Fourier restriction via efficient congruencing . Int. Math. Res. Not.(2017), no. 5, 13421389. https://doi.org/10.1093/imrn/rnw031.
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Canadian Mathematical Bulletin
  • ISSN: 0008-4395
  • EISSN: 1496-4287
  • URL: /core/journals/canadian-mathematical-bulletin
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