no. 3
Multiplier conditions for Boundedness into Hardy spaces
[Sur une condition de multiplicateur de continuité a l’espace de Hardy]
Grafakos, Loukas1 ; Nakamura, Shohei2 ; Nguyen, Hanh Van3 ; Sawano, Yoshihiro4
1 Department of Mathematics University of Missouri Columbia, MO 65211 (USA)
2 Department of Mathematics Osaka University Toyonaka 560-0043, Osaka (Japan)
3 Department of Mathematics University of Alabama Tuscaloosa, AL 35487 (USA)
4 Department of Mathematics Chuo University Kasuga, Bunkyo-ku, 112-8551, Tokyo (Japan)
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

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 :
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DOI : 10.5802/aif.3416
Classification : 10X99, 14A12, 11L05
Keywords: multiplier, multilinear, Hardy spaces
Mot clés : multiplicateur, multilineaire, espaces de Hardy

Grafakos, Loukas 1 ; Nakamura, Shohei 2 ; Nguyen, Hanh Van 3 ; Sawano, Yoshihiro 4

1 Department of Mathematics University of Missouri Columbia, MO 65211 (USA)
2 Department of Mathematics Osaka University Toyonaka 560-0043, Osaka (Japan)
3 Department of Mathematics University of Alabama Tuscaloosa, AL 35487 (USA)
4 Department of Mathematics Chuo University Kasuga, Bunkyo-ku, 112-8551, Tokyo (Japan)
Licence : CC-BY-ND 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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     title = {Multiplier conditions for {Boundedness} into {Hardy} spaces},
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Grafakos, Loukas; Nakamura, Shohei; Nguyen, Hanh Van; Sawano, Yoshihiro. Multiplier conditions for Boundedness into Hardy spaces. Annales de l'Institut Fourier, Tome 71 (2021) no. 3, pp. 1047-1064. doi : 10.5802/aif.3416. https://aif.centre-mersenne.org/articles/10.5802/aif.3416/

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