Abstract
In this paper we prove a sharp trilinear inequality which is motivated by a program to obtain the sharp form of the $L^2 - L^6$ Tomas-Stein adjoint restriction inequality on the circle. Our method uses intricate estimates for integrals of sixfold products of Bessel functions developed in a companion paper. We also establish that constants are local extremizers of the Tomas-Stein adjoint restriction inequality as well as of another inequality appearing in the program.
Original language | English |
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Pages (from-to) | 1463–1486 |
Number of pages | 24 |
Journal | Revista Matematica Iberoamericana |
Volume | 33 |
Issue number | 4 |
DOIs | |
Publication status | Published - 2017 |
Bibliographical note
19 pages, 2 tablesKeywords
- math.CA
- 42B10
- Circle
- Fourier restriction
- Sharp inequalities
- Extremizers
- Convolution of surface measures
- Bessel functions