A variational restriction theorem

Abstract

We establish variational estimates related to the problem of restricting the Fourier transform of a three-dimensional function to the two-dimensional Euclidean sphere. At the same time, we give a short survey of the recent field of maximal Fourier restriction theory.

10 pages, v2: bibliography is updated, a short survey of the maximal Fourier restriction is included, v3: introduction is reorganized according to referee's suggestions

References in corpus (7)

• A bootstrapping approach to jump inequalities and their applications
• Norm-variation of ergodic averages with respect to two commuting transformations
• A maximal restriction theorem and Lebesgue points of functions in F(L^p)
• Fourier restriction implies maximal and variational Fourier restriction
• An $L^4$ estimate for a singular entangled quadrilinear form
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Cited by in corpus (3)

• Fourier restriction implies maximal and variational Fourier restriction
• Uniform Fourier restriction for convex curves
• Multi-parameter maximal Fourier restriction