An interpolation technique towards the subpolynomial constants in the multilinear Bohnenblust-Hille inequality

TL;DR

This paper demonstrates that a recent interpolation method can recover the best known constants in the multilinear Bohnenblust-Hille inequality, surpassing the exponential growth limitations of previous approaches.

Contribution

It introduces an interpolation technique that achieves subpolynomial constants in the Bohnenblust-Hille inequality, improving upon prior exponential bounds.

Findings

Interpolation method recovers optimal constants

Previous approaches only achieved exponential bounds

New proof simplifies understanding of constants in the inequality

Abstract

We show that a recent interpolative new proof of the Bohnenblust--Hille inequality, when suitably handled, recovers its best known constants. This seems to be unexpectedly surprising since the known interpolative approaches only provide constants having exponential growth. This preprint is no longer an independent submission, it is now contained in the preprint arXiv 1310.2834.