Multiplier conditions for Boundedness into Hardy spaces
[Sur une condition de multiplicateur de continuité a l’espace de Hardy]
Annales de l'Institut Fourier, Online first, 18 p.

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

σ(ξ 1 ,...,ξ m )

et leurs dérivées s’annulent sur l’hyperplan ξ 1 ++ξ 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

σ(ξ 1 ,...,ξ m )

and their derivatives vanish on the hyperplane ξ 1 ++ξ m =0.

Reçu le :
Révisé le :
Accepté le :
Première publication :
DOI : https://doi.org/10.5802/aif.3416
Classification : 10X99,  14A12,  11L05
Mots clés : multiplicateur, multilineaire, espaces de Hardy
@unpublished{AIF_0__0_0_A19_0,
     author = {Grafakos, Loukas and Nakamura, Shohei and Nguyen, Hanh Van and Sawano, Yoshihiro},
     title = {Multiplier conditions for {Boundedness} into {Hardy} spaces},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     year = {2021},
     doi = {10.5802/aif.3416},
     language = {en},
     note = {Online first},
}
Grafakos, Loukas; Nakamura, Shohei; Nguyen, Hanh Van; Sawano, Yoshihiro. Multiplier conditions for Boundedness into Hardy spaces. Annales de l'Institut Fourier, Online first, 18 p.

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