Factorization in Fourier restriction theory and near extremizers

In Fourier restriction theory, so‐called Maurey–Nikishin–Pisier factorization has often been used as a convenient off‐the‐shelf means to prove certain factorizations of the Fourier restriction operator. We give an alternative approach to such factorizations in Fourier restriction theory. Based on an induction‐on‐scales argument, our comparably simple method applies to any compact quadratic surface, in particular compact parts of the paraboloid and the hyperbolic paraboloid. This is achieved by constructing near extremizers with big “mass,” which itself might be of interest.