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Fourier Restriction Conjecture

The Fourier restriction conjecture predicts sharp Lp-space estimates for the Fourier restriction operator on curved surfaces. One standard sphere formulation, written using the dual Fourier extension operator, asserts

||E_(S^(n-1))g||_(L^q(R^n))<=C_q||g||_(L^infty(S^(n-1)))

for every q>2n/(n-1), with n>=2 and the usual surface measure.

See also

Bochner-Riesz Conjecture, Fourier Extension Operator, Fourier Restriction Operator, Kakeya Maximal Conjecture

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References

Stein, E. M. Harmonic Analysis. Princeton, NJ: Princeton University Press, 1993.

Cite this as:

Weisstein, Eric W. "Fourier Restriction Conjecture." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/FourierRestrictionConjecture.html

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