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2007 Unboundedness of the ball bilinear multiplier operator
Geoff Diestel, Loukas Grafakos
Nagoya Math. J. 185: 151-159 (2007).

Abstract

For all $n > 1$, the characteristic function of the unit ball in $\mathbb{R}^{2n}$ is not the symbol of a bounded bilinear multiplier operator from $L^{p}(\mathbb{R}^{n}) \times L^{q}(\mathbb{R}^{n})$ to $L^{r}(\mathbb{R}^{n})$ when $1/p+1/q = 1/r$ and exactly one of $p$, $q$, or $r' = r/(r-1)$ is less than $2$.

Citation

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Geoff Diestel. Loukas Grafakos. "Unboundedness of the ball bilinear multiplier operator." Nagoya Math. J. 185 151 - 159, 2007.

Information

Published: 2007
First available in Project Euclid: 23 March 2007

zbMATH: 1131.43003
MathSciNet: MR2301463

Subjects:
Primary: 42B25 , 43B20
Secondary: 46B70 , 47B38

Keywords: bilinear Hilbert transform , multilinear operators

Rights: Copyright © 2007 Editorial Board, Nagoya Mathematical Journal

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