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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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On extremizers for Strichartz estimates for higher order Schrödinger equations
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by Diogo Oliveira e Silva and René Quilodrán PDF
Trans. Amer. Math. Soc. 370 (2018), 6871-6907 Request permission


For an appropriate class of convex functions $\phi$, we study the Fourier extension operator on the surface {(𝑦,|𝑦|²+𝜙(𝑦)):𝑦∈ℝ


equipped with projection measure. For the corresponding extension inequality, we compute optimal constants and prove that extremizers do not exist. The main tool is a new comparison principle for convolutions of certain singular measures that holds in all dimensions. Using tools of concentration-compactness flavor, we further investigate the behavior of general extremizing sequences. Our work is directly related to the study of extremizers and optimal constants for Strichartz estimates of certain higher order Schrödinger equations. In particular, we resolve a dichotomy from the recent literature concerning the existence of extremizers for a family of fourth order Schrödinger equations and compute the corresponding operator norms exactly where only lower bounds were previously known.

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Additional Information
  • Diogo Oliveira e Silva
  • Affiliation: Hausdorff Center for Mathematics, 53115 Bonn, Germany
  • MR Author ID: 756024
  • Email:
  • René Quilodrán
  • Affiliation: Departamento de Ciencias Exactas, Universidad de Los Lagos, Avenida Fuchslocher 1305, Osorno, Chile
  • Email:
  • Received by editor(s): June 13, 2016
  • Received by editor(s) in revised form: December 26, 2016
  • Published electronically: February 26, 2018
  • Additional Notes: The first author was partially supported by the Hausdorff Center for Mathematics.
  • © Copyright 2018 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 370 (2018), 6871-6907
  • MSC (2010): Primary 42B10
  • DOI:
  • MathSciNet review: 3841835