Abstract
We prove in this paper one weight norm inequalities for some positive Bergman-type operators.
Similar content being viewed by others
References
Békollé, D.: Inégalités à poids pour le project de Bergman dans la boule unité de \({\mathbb{C}}^n\), Studia Math. 71 (1981/82), no. 3, 305–323 (French)
Békollé, D., Bonami, A.: Inégalités à poids pour le noyau de Bergman, C. R. Acad. Sci. Paris Sér. A-B 286 (1978), no. 18, A775–A778 (French, with English summary)
Cruz-Uribe, D.: Elementary proofs of one weight norm inequalities for fractional integral operators and commutators. Harmonic analysis, partial differential equations, Banach spaces, and operator theory, vol. 2, pp. 183–198, Association of Women in Mathematics, 5. Springer, Cham (2017). arXiv:1507.02559
Dondjio, C., Sehba, B.F.: Maximal function and Carleson measures in the theory of Békollé–Bonami weights. Colloq. Math. 142(2), 211–226 (2016)
Lacey, M., Moen, K., Pérez, C., Torres, R.H.: Sharp weighted bounds for fractional integral operators. J. Funct. Anal. 259(5), 1073–1097 (2010)
Muckenhoupt, B., Wheeden, R.L.: Weighted norm inequalities for fractional integrals. Trans. Am. Math. Soc. 192, 261–274 (1974)
Pott, S., Reguera, M.C.: Sharp Békollé estimates for the Bergman projection. J. Funct. Anal. 265(12), 3233–3244 (2013)
Sehba, B.F.: Sharp off-diagonal weighted norm inequalities for the Bergman projection. arXiv:1703.00275
Sehba, B.F.: Weighted boundedness of maximal functions and fractional Bergman operators. J. Geom. Anal. 28(2), 1635–1664 (2018)
Acknowledgements
The author would like to thank the anonymous referees for carefully reading the manuscript and making suggestions that improved the presentation of the paper.
Author information
Authors and Affiliations
Corresponding author
Additional information
Communicated by Stephane Jaffard.
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Sehba, B.F. Weighted Norm Inequalities for Fractional Bergman Operators. Constr Approx 51, 225–245 (2020). https://doi.org/10.1007/s00365-019-09470-5
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00365-019-09470-5