Decoupling inequalities for quadratic forms

Abstract

We prove sharp ${\ell }^q{L}^p$ decoupling inequalities for $p,q\in [2,\infty )$ and arbitrary tuples of quadratic forms. Connections to prior results on decoupling inequalities for quadratic forms are also explained. We also include some applications of our results to exponential sum estimates and to Fourier restriction estimates. The proof of our main result is based on scale-dependent Brascamp--Lieb inequalities.

v2: corrected following referee reports, 37 pages

References in corpus (1)

• Bilinear restriction estimates for surfaces of codimension bigger than one

Cited by in corpus (2)

• Regularized Brascamp--Lieb inequalities
• Fourier decay of fractal measures on surfaces of co-dimension two in ${\mathbb{R}}^5$