Multilinear Fourier multipliers with minimal Sobolev regularity, I

Loukas Grafakos, and Hanh Van Nguyen. "Multilinear Fourier multipliers with minimal Sobolev regularity, I." Colloquium Mathematicae 144.1 (2016): 1-30. <http://eudml.org/doc/284167>.

@article{LoukasGrafakos2016,
abstract = {We find optimal conditions on m-linear Fourier multipliers that give rise to bounded operators from products of Hardy spaces $H^\{p_\{k\}\}$, $0 < p_\{k\} ≤ 1$, 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.},
author = {Loukas Grafakos, Hanh Van Nguyen},
journal = {Colloquium Mathematicae},
keywords = {multilinear Fourier multipliers; Hardy spaces; -based Sobolev spaces},
language = {eng},
number = {1},
pages = {1-30},
title = {Multilinear Fourier multipliers with minimal Sobolev regularity, I},
url = {http://eudml.org/doc/284167},
volume = {144},
year = {2016},
}

TY - JOUR
AU - Loukas Grafakos
AU - Hanh Van Nguyen
TI - Multilinear Fourier multipliers with minimal Sobolev regularity, I
JO - Colloquium Mathematicae
PY - 2016
VL - 144
IS - 1
SP - 1
EP - 30
AB - We find optimal conditions on m-linear Fourier multipliers that give rise to bounded operators from products of Hardy spaces $H^{p_{k}}$, $0 < p_{k} ≤ 1$, 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.
LA - eng
KW - multilinear Fourier multipliers; Hardy spaces; -based Sobolev spaces
UR - http://eudml.org/doc/284167
ER -