One of the nice applications of decoupling is Bourgain’s record towards Lindelöf:
Wooley has developed some techniques known as efficient congruencing which allow one to obtain estimates also derived from decoupling.
Lets call ’efficient boxing’ using Wooley’s efficient congruencing methods with archimedian metric instead of p-adic.
My question is: It is possible to use efficient boxing to recover the mean value estimate from the above Bourgain paper?
Some background about this: A direction along these lines was initiated by Watt
so a similar question: Can Wooley’s innovations be combined with Watt’s ideas to recover Bourgain’s result?