Multilinear Fourier multipliers with minimal Sobolev regularity, I

Loukas Grafakos; Hanh Van Nguyen

Colloquium Mathematicae, Tome 144 (2016), p. 1-30 / Harvested from The Polish Digital Mathematics Library

Résumé

We find optimal conditions on m-linear Fourier multipliers that give rise to bounded operators from products of Hardy spaces $H^{p_{k}}$ , $0 < p_{k} \leq 1$ , to Lebesgue spaces $L^{p}$ . These conditions are expressed in terms of L²-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.

Publié le : 2016-01-01

Zbl 1339.42012

EUDML-ID : urn:eudml:doc:284167

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     author = {Loukas Grafakos and Hanh Van Nguyen},
     title = {Multilinear Fourier multipliers with minimal Sobolev regularity, I},
     journal = {Colloquium Mathematicae},
     volume = {144},
     year = {2016},
     pages = {1-30},
     zbl = {1339.42012},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm6771-10-2015}
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Loukas Grafakos; Hanh Van Nguyen. Multilinear Fourier multipliers with minimal Sobolev regularity, I. Colloquium Mathematicae, Tome 144 (2016) pp. 1-30. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm6771-10-2015/