Geodesic
Multilinear Fourier multipliers with minimal Sobolev regularity, I
Loukas Grafakos 1   ; Hanh Van Nguyen 1
1 Department of Mathematics University of Missouri Columbia, MO 65211, U.S.A.
Colloquium Mathematicum, Tome 144 (2016) no. 1, pp. 1-30 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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We find optimal conditions on $m$-linear Fourier multipliers that give rise to bounded operators from products of Hardy spaces $H^{p_k}$, $0 \lt p_k\le 1$, to Lebesgue spaces $L^p$. These conditions are expressed in terms of $L^2$-based Sobolev spaces with sharp indices within the classes of multipliers we consider. Our results extend those obtained in the linear case ($m=1 $) by Calderón and Torchinsky (1977) and in the bilinear case ($m=2$) by Miyachi and Tomita (2013). We also prove a coordinate-type Hörmander integral condition which we use to obtain certain endpoint cases.
DOI : 10.4064/cm6771-10-2015
Keywords: optimal conditions m linear fourier multipliers rise bounded operators products hardy spaces lebesgue spaces these conditions expressed terms based sobolev spaces sharp indices within classes multipliers consider results extend those obtained linear calder torchinsky bilinear miyachi tomita prove coordinate type ormander integral condition which obtain certain endpoint cases

Loukas Grafakos  1   ; Hanh Van Nguyen  1

1 Department of Mathematics University of Missouri Columbia, MO 65211, U.S.A. 
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Loukas Grafakos; Hanh Van Nguyen. Multilinear Fourier multipliers with minimal Sobolev regularity, I. Colloquium Mathematicum, Tome 144 (2016) no. 1, pp. 1-30. doi: 10.4064/cm6771-10-2015

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