Abstract
We provide in this note some endpoint criteria for the boundedness of some general multilinear operators with positive kernel. We also study boundedness properties of a family of multilinear Bergman-type operators on product of upper-half planes.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bansah, J., Sehba, B.F.: Boundedness of a family of Hilbert-type operators and its Bergman-type analogue. Illinois J. Math. 59(4), 949–977 (2015)
Bansah, J., Sehba, B.F.: Boundedness criteria and norm of some multilinear Hilbert-type operators. Abstr. Appl. Anal. (2017). https://doi.org/10.1155/2017/6829093
Békollé, D., Bonami, A., Garrigós, G., Nana, C., Peloso, M., Ricci, F.: Lecture notes on Bergman projectors in tube domains over cones: an analytic and geometric viewpoint. In: IMHOTEP, Exposé I, Proceedings of the International Workshop in Classical Analysis, Yaoundé 5 (2004)
Békollé, D., Bonami, A., Peloso, M., Ricci, F.: Boundedness of Bergman projections on tube domains over light cones. Math. Z. 237, 31–59 (2001)
Grafakos, L., Torres, R.: A multilinear Schur test and multiplier operators. J. Funct. Anal. 187, 1–24 (2001)
Jectić, M., Pavlović, M., Shamoyan, R.A.: Note on the diagonal mapping in spaces of analytic functions in the unit polydiscc. Publ. Math. Debr. 74(1–2), 1–14 (2009)
Okikiolu, G.O.: On inequalities for integral operators. Glasg. Math. J. 11(2), 126–133 (1969)
Ren, G., Shi, J.: The diagonal mapping in mixed norm spaces. Stud. Math. 163(2), 103–117 (2004)
Sehba, B.F.: Bergman type operators in tubular domains over symmetric cones. Proc. Edin. Math. Soc. 52(2), 529–544 (2009)
Shapiro, J.H.: Mackey topologies, reproducing kernels, and diagonal maps on the Hardy and Bergman spaces. Duke Math. J. 43(1), 187–202 (1976)
Zhao, R.: Generalization of Schur’s Test and its application to a class of integral operators on the unit ball of \(C^n\). Integr. Equ. Oper. Theory 82(4), 519–532 (2015)
Author information
Authors and Affiliations
Contributions
The authors would like to thank the referee for carefully reading the manuscript and for comments and suggestions that have helped improving the presentation of this work.
Corresponding author
Ethics declarations
Conflict of interest
The authors declare that they have no conflicting interest with respect to this work.
Additional information
Communicated by Adrian Constantin.
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Asare-Tuah, A., Gonessa, J. & Sehba, B.F. Multilinear Schur-type tests and boundedness of multilinear Bergman-type operators. Monatsh Math 201, 11–51 (2023). https://doi.org/10.1007/s00605-023-01852-z
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00605-023-01852-z