Advertisement

Results in Mathematics

, 74:43 | Cite as

Off-Diagonal Boundedness and Unboundedness of Product Bergman-Type Operators

  • Justice Sam Bansah
  • Benoît Florent SehbaEmail author
Article
  • 7 Downloads

Abstract

In this paper we discuss boundedness and unboundedness of Bergman-type operators on product of upper-half planes. A new product version of the Okikiolu’s theorem and Cayley’s transform play a crucial role in the proof of the results.

Keywords

Bergman projection upper-half plane Gamma function 

Mathematics Subject Classification

Primary 32A36 32A37 47B35 Secondary 32M15 

Notes

References

  1. 1.
    Bansah, J.S., Sehba, B.F.: Bondedness of a family of Hilbet-type operators and its Bergman-type analogue. Illinois J. Math. 59(4), 949–977 (2015)MathSciNetzbMATHGoogle Scholar
  2. 2.
    Beals, R., Wong, R.: Special Functions. Cambridge University Press, Cambridge (2010)CrossRefGoogle Scholar
  3. 3.
    Cheng, G., Fang, X., Wang, Z., Yu, J.: The hyper-singular cousin of the Bergman projection. Trans. Am. Math. Soc. 369(12), 8643–8662 (2017)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Liu, C., Liu, Y., Hu, P., Zhou, L.: Two classes of integral operators over the Siegel upper half-space. Complex Anal. Oper. Theory (2018).  https://doi.org/10.1007/s11785-018-0785-6 CrossRefGoogle Scholar
  5. 5.
    Liu, C., Si, J., Hu, P.: \(L^p\)-\(L^q\) boundedness of Bergman-type operators over the Siegel upper half-space. J. Math. Anal. Appl. 464(2), 1203–1212 (2018)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Nana, C.: Sharp estimates for operators with positive Bergman kernel in homogeneous Siegel domains of \(\mathbb{C}^n\). arXiv:1803.07839v1
  7. 7.
    Okikiolu, G.O.: On inequalities for integral operators. Glasg. Math. J. 2, 126–133 (1970)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Sehba, B.F.: On the bondedness of the fractional Bergman operators. Abstr. Appl. Anal. Art. ID 8363478 (2017)Google Scholar
  9. 9.
    Sehba, B.F.: Off-diagonal weighted norm estimate for the Bergman projection. arXiv:1703.0027v4
  10. 10.
    Sawyer, E., Wang, Z.: Weighted inequalities for product fractional integrals. arXiv:1702.03870
  11. 11.
    Sawyer, E., Wang, Z.: The \(\theta \)-bump theorem for product fractional integrals. arXiv:1803.09500
  12. 12.
    Tanaka, H., Yabuta, K.: The n-linear embedding theorem for dyadic rectangles. arXiv:1710.08059
  13. 13.
    Zhao, R.: Generalization of Schurs test and its application to a class of integral operators on the unit ball of \(\mathbb{C}^n\). Integral Equ. Oper. Theory 82(4), 519–532 (2015)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of GhanaLegon AccraGhana

Personalised recommendations