Weighted norm inequalities for derivatives on Bergman spaces
Annales de l'Institut Fourier, Online first, 24 p.

An equivalent norm in the weighted Bergman space A ω p , induced by an ω in a certain large class of non-radial weights, is established in terms of higher order derivatives. Other Littlewood–Paley inequalities are also considered. On the way to the proofs, we characterize the q-Carleson measures for the weighted Bergman space A ω p and the boundedness of a Hörmander-type maximal function. Results obtained are further applied to describe the resolvent set of the integral operators T g (f)(z)= 0 z g (ζ)f(ζ)dζ acting on A ω p .

Nous construisons une norme équivalente, définie à l’aide des dérivées supérieures, dans un espace de Bergman pondéré A ω p ω appartient à une large classe des poids non radiaux. Nous analysons aussi autres inégalités de Littlewood–Paley. Avant de démontrer les résultats principaux nous caractérisons les q-mesures de Carleson sur les espaces A ω p et montrons que la fonction maximale de Hörmander est bornée. En utilisant nos résultats nous pouvons décrire l’ensemble résolvant de l’opérateur intégral T g (f)(z)= 0 z g (ζ)f(ζ)dζ agissant sur A ω p .

Received:
Revised:
Accepted:
Online First:
DOI: 10.5802/aif.3632
Classification: 30H20, 47G10
Keywords: Bergman space, Carleson measure, integral operator, Littlewood–Paley inequality, Hörmander-type maximal function, resolvent set.
Mot clés : Espace de Bergman, mesure de Carleson, opérateur intégral, inégalité de Littlewood–Paley, fonction maximale de Hörmander, ensemble résolvant.
Peláez, José Ángel 1; Rättyä, Jouni 2

1 Departamento de Análisis Matemático, Universidad de Málaga, Campus de Teatinos, 29071 Málaga, (Spain)
2 University of Eastern Finland, P.O.Box 111, 80101 Joensuu (Finland)
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Peláez, José Ángel; Rättyä, Jouni. Weighted norm inequalities for derivatives on Bergman spaces. Annales de l'Institut Fourier, Online first, 24 p.

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