A note on bi-linear multipliers

Shrivastava, Saurabh

doi:10.1090/S0002-9939-2015-12679-2

A note on bi-linear multipliers
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by Saurabh Shrivastava PDF

Proc. Amer. Math. Soc. 143 (2015), 3055-3061 Request permission

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 $\mathbb {R}^d.$

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