Multilinear Fourier multipliers with minimal Sobolev regularity, I

• Autorzy: Loukas Grafakos , Hanh Van Nguyen
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 42B15: Multipliers
• 42B30: H p -spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2016
• Tom: 144
• Numer: 1
• Strony: 1-30

Daty

wydano

2016

Twórcy

autor

Loukas Grafakos

• Department of Mathematics, University of Missouri, Columbia, MO 65211, U.S.A.

autor

Hanh Van Nguyen

• Department of Mathematics, University of Missouri, Columbia, MO 65211, U.S.A.

Identyfikatory

DOI

10.4064/cm6771-10-2015