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Multilinear Fourier multipliers with minimal Sobolev regularity, I

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Grafakos L., Nguyen H.

Colloquium Mathematicum

2016

tom 144

nr 1

1-30

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.

Ograniczanie wyników

1 Colloquium Mathematicum

1 Grafakos L.

1 Nguyen H.

1 2016

Wyniki wyszukiwania

Multilinear Fourier multipliers with minimal Sobolev regularity, I