We prove sharp decoupling inequalities for all degenerate surfaces of codimension two in R 5 given by two quadratic forms in three variables. Together with previous work by Demeter, Guo, and Shi in the non-degenerate case, this provides a classification of decoupling inequalities for pairs of quadratic forms in three variables.
We run an iteration argument due to Pramanik and Seeger [PS07], to provide a proof of sharp decoupling inequalities for conical surfaces and for k-cones. These are extensions of results of Laba and Pramanik [LP06] to sharp exponents.
We prove sharp q L p decoupling inequalities for arbitrary tuples of quadratic forms. Our argument is based on scale-dependent Brascamp-Lieb inequalities.
We improve the L p (R n ) bounds on Stein's square function to the best known range of the Fourier restriction problem when n ≥ 4. Applications including certain local smoothing estimates are also discussed.
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