Browsing by Subject "decoupling"

The purpose of this thesis is to act as a guide for the 2017 article A study guide for the l^2 decoupling theorem by J. Bourgain and C. Demeter. However, this thesis is self-sufficient. The aim has been to give a detailed presentation and handle the weight exponent E especially carefully in the arguments. We begin by presenting the decoupling inequality of the l^2 decoupling theorem and the associated Fourier transform -like operator. The theorem concerns finding a satisfactory upper bound for the decoupling constant related to the inequality. We also list some general results that a graduate student might not be very familiar with; among them are a few consequences of Hölder's inequality. We move on to study the properties of the weight functions that we use in the L^p-norms in the decoupling. We present two operator lemmas to which we can reduce many of our arguments. The other lemma gives us the opportunity to use certain Schwartz functions in our proofs. We then move on to prove the l^2 decoupling theorem in the lower range 2<= p <= (2n)/(n-1). This includes the definition of multilinear decoupling constants and an iterative process.