Sharp maximal estimates for doubly oscillatory integrals
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- by Björn Gabriel Walther PDF
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Abstract:
We study doubly oscillatory integrals \[ \int _{\mathbf R^n} e^{i(\xi + y|\xi | + t|\xi |^ a)} \widehat f(\xi ) d\xi \] and prove a sharp maximal estimate which is an immediate consequence of a well-known conjecture in Fourier analysis on $\mathbf {R}^n$.References
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Additional Information
- Björn Gabriel Walther
- Affiliation: Department of Mathematics, Royal Institute of Technology, SE – 100 44 Stockholm, Sweden
- Address at time of publication: Department of Mathematics, Brown University, Providence, Rhode Island 02912–1917
- Email: WALTHER@Math.KTH.SE, WALTHER@Math.Brown.Edu
- Received by editor(s): August 10, 2000
- Received by editor(s) in revised form: July 19, 2001
- Published electronically: May 1, 2002
- Additional Notes: This paper is a revision of [16, Chapter 9]. The author would like to thank Professor Per Sjölin, Royal Institute of Technology, Stockholm, Sweden, for patience and support. The final draft was made during visits at Brown University, Providence, RI, USA, and Univerzita Komenského, Bratislava, Slovakia.
- Communicated by: Christopher D. Sogge
- © Copyright 2002 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 130 (2002), 3641-3650
- MSC (1991): Primary 42B25, 42B99, 35L05, 35J10, 35Q40
- DOI: https://doi.org/10.1090/S0002-9939-02-06527-9
- MathSciNet review: 1920044