An equivalent norm in the weighted Bergman space , induced by an 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 -Carleson measures for the weighted Bergman space and the boundedness of a Hörmander-type maximal function. Results obtained are further applied to describe the resolvent set of the integral operators acting on .
Nous construisons une norme équivalente, définie à l’aide des dérivées supérieures, dans un espace de Bergman pondéré où 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 -mesures de Carleson sur les espaces et montrons que la fonction maximale de Hörmander est bornée. En utilisant nos résultats nous pouvons décrire l’ensemble résolvant de l’opérateur intégral agissant sur .
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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
@article{AIF_2024__74_4_1721_0, author = {Pel\'aez, Jos\'e \'Angel and R\"atty\"a, Jouni}, title = {Weighted norm inequalities for derivatives on {Bergman} spaces}, journal = {Annales de l'Institut Fourier}, pages = {1721--1744}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {74}, number = {4}, year = {2024}, doi = {10.5802/aif.3632}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.3632/} }
TY - JOUR AU - Peláez, José Ángel AU - Rättyä, Jouni TI - Weighted norm inequalities for derivatives on Bergman spaces JO - Annales de l'Institut Fourier PY - 2024 SP - 1721 EP - 1744 VL - 74 IS - 4 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.3632/ DO - 10.5802/aif.3632 LA - en ID - AIF_2024__74_4_1721_0 ER -
%0 Journal Article %A Peláez, José Ángel %A Rättyä, Jouni %T Weighted norm inequalities for derivatives on Bergman spaces %J Annales de l'Institut Fourier %D 2024 %P 1721-1744 %V 74 %N 4 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.3632/ %R 10.5802/aif.3632 %G en %F AIF_2024__74_4_1721_0
Peláez, José Ángel; Rättyä, Jouni. Weighted norm inequalities for derivatives on Bergman spaces. Annales de l'Institut Fourier, Volume 74 (2024) no. 4, pp. 1721-1744. doi : 10.5802/aif.3632. https://aif.centre-mersenne.org/articles/10.5802/aif.3632/
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