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Damping estimates for oscillatory integral operators with real-analytic phases and its applications

  • Zuoshunhua Shi EMAIL logo , Shaozhen Xu and Dunyan Yan
Published/Copyright: April 6, 2019
Forum Mathematicum
From the journal Forum Mathematicum Volume 31 Issue 4

Abstract

In this paper, we investigate sharp damping estimates for a class of one-dimensional oscillatory integral operators with real-analytic phases. By establishing endpoint estimates for suitably damped oscillatory integral operators, we are able to give a new proof of the sharp Lp estimates, which have been proved by Xiao in [Endpoint estimates for one-dimensional oscillatory integral operators, Adv. Math. 316 2017, 255–291]. The damping estimates obtained in this paper are of independent interest.

Keywords: Oscillatory integral operator; real-analytic phase; damped oscillatory integral operator; Newton polyhedron; van der Corput lemma
MSC 2010: 42B20; 47G10

Communicated by Christopher D. Sogge

Funding source: National Natural Science Foundation of China

Award Identifier / Grant number: 11701573

Award Identifier / Grant number: 11871452

Funding statement: This work was supported in part by the National Natural Science Foundation of China under Grant numbers 11701573 and 11871452.

Acknowledgements

Part of this work was done when the first author was visiting the Department of Mathematics, Beijing Normal University. He would like to thank H. L. Tang for his valuable discussions and appreciates the hospitality and the support from Beijing Normal University. The second author gratefully acknowledges the financial support from China Scholarship Council. We would also like to express our gratitude to Professor Xiaochun Li for his valuable comments and warm encouragement.

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Received: 2019-01-09
Revised: 2019-02-27
Published Online: 2019-04-06
Published in Print: 2019-07-01

© 2019 Walter de Gruyter GmbH, Berlin/Boston

Articles in the same Issue

  1. Frontmatter
  2. Characteristic functions of semigroups in semi-simple Lie groups
  3. Damping estimates for oscillatory integral operators with real-analytic phases and its applications
  4. Formality properties of finitely generated groups and Lie algebras
  5. Toric actions in cosymplectic geometry
  6. On classification of typical representations for GL3(F)
  7. Integrable generators of Lie algebras of vector fields on ℂn
  8. Expanding phenomena over matrix rings
  9. On sup-norm bounds part II: GL(2) Eisenstein series
  10. Sublinear elliptic problems under radiality. Harmonic NA groups and Euclidean spaces
  11. Partial and full boundary regularity for non-autonomous functionals with Φ-growth conditions
  12. Radial averaging operator acting on Bergman and Lebesgue spaces
  13. The 𝑝-adic variation of the Gross–Kohnen–Zagier theorem
https://doi.org/10.1515/forum-2019-0011
Keywords for this article
Oscillatory integral operator; real-analytic phase; damped oscillatory integral operator; Newton polyhedron; van der Corput lemma

Articles in the same Issue

  1. Frontmatter
  2. Characteristic functions of semigroups in semi-simple Lie groups
  3. Damping estimates for oscillatory integral operators with real-analytic phases and its applications
  4. Formality properties of finitely generated groups and Lie algebras
  5. Toric actions in cosymplectic geometry
  6. On classification of typical representations for GL3(F)
  7. Integrable generators of Lie algebras of vector fields on ℂn
  8. Expanding phenomena over matrix rings
  9. On sup-norm bounds part II: GL(2) Eisenstein series
  10. Sublinear elliptic problems under radiality. Harmonic NA groups and Euclidean spaces
  11. Partial and full boundary regularity for non-autonomous functionals with Φ-growth conditions
  12. Radial averaging operator acting on Bergman and Lebesgue spaces
  13. The 𝑝-adic variation of the Gross–Kohnen–Zagier theorem
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