Restriction theorems for the Fourier transform to homogeneous polynomial surfaces in ℝ³
E. Ferreyra, T. Godoy, M. Urciuolo (2004)
Studia Mathematica
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Let φ:ℝ² → ℝ be a homogeneous polynomial function of degree m ≥ 2, let Σ = (x,φ(x)): |x| ≤ 1 and let σ be the Borel measure on Σ defined by where B is the unit open ball in ℝ² and dx denotes the Lebesgue measure on ℝ². We show that the composition of the Fourier transform in ℝ³ followed by restriction to Σ defines a bounded operator from to for certain p,q. For m ≥ 6 the results are sharp except for some border points.