A note on bi-linear multipliers

Abstract

In this paper we prove that if $\chi _{_E}(\xi -\eta )$ – the indicator function of a measurable set $E\subseteq \mathbb {R}^d$ – is a bi-linear multiplier symbol for exponents $p,q,r$ satisfying the Hölder’s condition $\frac {1}{p}+\frac {1}{q}=\frac {1}{r}$ and exactly one of $p,q,$ or $r’=\frac {r}{r-1}$ is less than $2,$ then $E$ is equivalent to an open subset of $\mathbb {R}^d.$

Locations

• Proceedings of the American Mathematical Society - View
• arXiv (Cornell University) - View - PDF