Multiplier conditions for Boundedness into Hardy spaces

Grafakos, Loukas; Nakamura, Shohei; Nguyen, Hanh Van; Sawano, Yoshihiro

Annales de l'Institut Fourier, Tome 71 (2021) no. 3, pp. 1047-1064.

Dans ce travail, on donne des conditions utilisables et explicites pour que des multiplicateurs linéaires et multilinéaires de type Coifman-Meyer, des sommes de produits d’opérateurs de Calderon-Zygmund, et aussi des opérateurs de type intermédiaire, soient bornés de produits d’espaces de Lebesgue ou de Hardy dans un espace de Hardy. Ces conditions affirment que les symboles des multiplicateurs

$$\sigma ({\xi }_1,...,{\xi }_m)$$

et leurs dérivées s’annulent sur l’hyperplan ${\xi }_1+\cdots +{\xi }_m=0$.

In the present work we find useful and explicit necessary and sufficient conditions for linear and multilinear multiplier operators of Coifman–Meyer type, finite sum of products of Calderón–Zygmund operators, and also of intermediate types to be bounded from a product of Lebesgue or Hardy spaces into a Hardy space. These conditions state that the symbols of the multipliers

$$\sigma ({\xi }_1,...,{\xi }_m)$$

and their derivatives vanish on the hyperplane ${\xi }_1+\cdots +{\xi }_m=0$.

Classification : 10X99, 14A12, 11L05
Keywords: multiplier, multilinear, Hardy spaces
Mot clés : multiplicateur, multilineaire, espaces de Hardy

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