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

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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.

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References

  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)

    Article  MathSciNet  Google Scholar 

  2. Beals, R., Wong, R.: Special Functions. Cambridge University Press, Cambridge (2010)

    Book  Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

  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

    Article  Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

  6. Nana, C.: Sharp estimates for operators with positive Bergman kernel in homogeneous Siegel domains of \(\mathbb{C}^n\). arXiv:1803.07839v1

  7. Okikiolu, G.O.: On inequalities for integral operators. Glasg. Math. J. 2, 126–133 (1970)

    Article  MathSciNet  Google Scholar 

  8. Sehba, B.F.: On the bondedness of the fractional Bergman operators. Abstr. Appl. Anal. Art. ID 8363478 (2017)

  9. Sehba, B.F.: Off-diagonal weighted norm estimate for the Bergman projection. arXiv:1703.0027v4

  10. Sawyer, E., Wang, Z.: Weighted inequalities for product fractional integrals. arXiv:1702.03870

  11. Sawyer, E., Wang, Z.: The \(\theta \)-bump theorem for product fractional integrals. arXiv:1803.09500

  12. Tanaka, H., Yabuta, K.: The n-linear embedding theorem for dyadic rectangles. arXiv:1710.08059

  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)

    Article  Google Scholar 

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  1. Department of Mathematics, University of Ghana, Legon, P. O. Box LG 62 , Legon Accra, Ghana

    Justice Sam Bansah & Benoît Florent Sehba

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  1. Justice Sam Bansah
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  2. Benoît Florent Sehba
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Correspondence to Benoît Florent Sehba.

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Bansah, J.S., Sehba, B.F. Off-Diagonal Boundedness and Unboundedness of Product Bergman-Type Operators. Results Math 74, 43 (2019). https://doi.org/10.1007/s00025-019-0965-3

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  • DOI: https://doi.org/10.1007/s00025-019-0965-3

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