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Some Inequalities for the Fourier Transform and Their Limiting Behaviour
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Some Inequalities for the Fourier Transform and Their Limiting Behaviour
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Journal Article
Some Inequalities for the Fourier Transform and Their Limiting Behaviour
2024
Overview
We identify a one-parameter family of inequalities for the Fourier transform whose limiting case is the restriction conjecture for the sphere. Using Stein’s method of complex interpolation, we prove the conjectured inequalities when the target space is
L
2
, and show that this recovers in the limit the celebrated Tomas-Stein theorem.
Publisher
Springer US,Springer Nature B.V
