Constants of the Kahane--Salem--Zygmund inequality asymptotically bounded by $1$ II

Abstract

In [18] we have shown that, for $p_1,p_2\in (2,\infty ]$, the constants of Bennett's inequality on unimodular bilinear forms on ${\ell }_{p_1}^{n_1}\times {\ell }_{p_2}^{n_2}$ are asymptotically bounded by $1$. In the present paper we use a different approximation technique to investigate the remaining cases $p_1,p_2\in [1,\infty ].$ This new approach also provides a stronger asymptotic control, in the sense that the constants are "uniformly" asymptotically bounded by $1$, with no dependence on $p_1,p_2.$

This paper is now incorporated to the new version of arXiv:2006.12892