Abstract
We prove \(\ell ^p\)-improving estimates for the averaging operator along the discrete paraboloid in the sharp range of p in all dimensions \(n\ge 2\).
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References
Anderson, T.C.: Quantitative \(\ell ^p\)-improving for discrete spherical averages along the primes. J. Fourier Anal. Appl. 26, 32 (2020)
Bourgain, J.: Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. I. Schrödinger equations. Geom. Funct. Anal. 3(2), 107–156 (1993)
Bourgain, J., Demeter, C.: The proof of the \(\ell ^2\) decoupling conjecture. Ann. Math. (2) 182(1), 351–389 (2015)
Demeter, C.: Fourier Restriction, Decoupling and Applications. Cambridge University Press, Cambridge (2020)
Han, R., Lacey, M. T., Yang, F.: Averages along the square integers: \(\ell ^p\) improving and sparse inequalities. Preprint (2019)
Han, R., Krause, B., Lacey, M. T., Yang, F.: Averages along the primes: improving and sparse bounds. Preprint (2019)
Han, R., Kovač, V., Lacey, M.T., Madrid, J., Yang, F.: Improving estimates for discrete polynomial averages. J. Fourier Anal. Appl. 26, 42 (2020)
Hughes, K.: \(\ell ^p\)-improving for discrete spherical averages. Ann. H. Lebesgue 3, 959–980 (2020)
Kesler, R.: \(\ell ^p({\mathbb{Z}}^d)\)-Improving properties and sparse bounds for discrete spherical maximal means, revisited. Preprint (2018)
Kesler, R., Lacey, M.T.: \(\ell ^p\)-improving inequalities for discrete spherical averages. Anal. Math. 46, 85–95 (2020)
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The authors would like to thank the anonymous referees for their careful reading of our manuscript and insightful comments and suggestions.
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Communicated by Hans G. Feichtinger.
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Ciprian Demeter is partially supported by the NSF Grant DMS-1800305. Bartosz Langowski is supported by the National Science Centre of Poland within the research Project OPUS 2017/27/B/ST1/01623.
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Dasu, S., Demeter, C. & Langowski, B. Sharp \(\ell ^p\)-Improving Estimates for the Discrete Paraboloid. J Fourier Anal Appl 27, 3 (2021). https://doi.org/10.1007/s00041-020-09801-2
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DOI: https://doi.org/10.1007/s00041-020-09801-2