Multipliers for Hardy spaces of Dirichlet series
[Multiplicateurs pour espaces de Hardy de séries de Dirichlet]
Fernandez Vidal, Tomas1 ; Galicer, Daniel1 ; Sevilla-Peris, Pablo2
1 Departamento de Matemática, Facultad de Cs. Exactas y Naturales, Universidad de Buenos Aires and IMAS-CONICET, Ciudad Universitaria, Pabellón I (C1428EGA) C.A.B.A. (Argentina)
2 Institut Universitari de Matemàtica Pura i Aplicada, Universitat Politècnica de València, Cmno Vera s/n 46022 València (Spain)
Annales de l'Institut Fourier, Online first, 37 p.

On charaterise l’espace de multiplicateurs de l’espace de Hardy de séries de Dirichlet ℋ p en ℋ q por tout 1≤p,q≤∞. Pour une série de Dirichlet fixée on analyse quelques proprietés estructurales de l’operateur de multiplication associé. Particularement on étude la norme, la norme essentielle et l’espectre d’un tell operateur. On utilise la identification naturell existant entre éspaces de séries de Dirichlet avec espaces de fonctions holomorphes en infinites variables, et on applique des méthodes de l’analyse complex et harmonique pur obtindre nous resultats. Comme consequence on trouve des resultats analogues pour telles espaces de fonctions holomorphes.

We characterise the space of multipliers from the Hardy space of Dirichlet series ℋ p into ℋ q for every 1≤p,q≤∞. For a fixed Dirichlet series, we also analyse some structural properties of its associated multiplication operator. In particular, we study the norm, the essential norm, and the spectrum for an operator of this kind. We exploit the existing natural identification of spaces of Dirichlet series with spaces of holomorphic functions in infinitely many variables and apply several methods from complex and harmonic analysis to obtain our results. As a byproduct we get analogous statements on such Hardy spaces of holomorphic functions.

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DOI : 10.5802/aif.3658
Classification : 30H10, 46G20, 30B50, 47A10
Keywords: Multipliers, Spaces of Dirichlet series, Hardy spaces, Infinite dimensional analysis.
Mot clés : Multiplicateur, espace de séries de Dirichlet, espace de Hardy, Analyse infini-dimensional.
Fernandez Vidal, Tomas 1 ; Galicer, Daniel 1 ; Sevilla-Peris, Pablo 2

1 Departamento de Matemática, Facultad de Cs. Exactas y Naturales, Universidad de Buenos Aires and IMAS-CONICET, Ciudad Universitaria, Pabellón I (C1428EGA) C.A.B.A. (Argentina)
2 Institut Universitari de Matemàtica Pura i Aplicada, Universitat Politècnica de València, Cmno Vera s/n 46022 València (Spain) 
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Fernandez Vidal, Tomas; Galicer, Daniel; Sevilla-Peris, Pablo. Multipliers for Hardy spaces of Dirichlet series. Annales de l'Institut Fourier, Online first, 37 p.

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