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Year 2020, Volume: 3 Issue: 1, 13 - 23, 25.03.2020

Job Bonyo

https://doi.org/10.33434/cams.631112

Abstract

References

  • [1] E. Albrecht, T. L. Miller, M. M. Neumann, Spectral properties of generalized Ces`aro operators on Hardy and weighted Bergman spaces. Arch. Math. (Basel), 85 (2005), 446–459.
  • [2] J. B. Garnett, Bounded Analytic Functions. Graduate Texts in Mathematics, Revised First Edition, Springer, Berlin, 2010.
  • [3] P. Duren, Theory of Hp spaces. Academic Press, New York, 1970.
  • [4] M. M. Peloso, Classical spaces of Holomorphic functions. Technical report, Universit di Milano, 2014.
  • [5] D. Bekolle, A.Bonimi. G. Garrigos, C. Nana, M. Peloso, F. Ricci, Lecture notes on Bergman projections in tube domais over cones: an analytic and geometric viewpoint, IMHOTEP J. Afr. Math. Pures Appl. 5 (2004). http://webs.um.es/gustavo.garrigos/papers/workshop5.pdf
  • [6] P. Duren, A. Schuster, Bergman spaces. Mathematical Surveys and Monographs 100, Amer. Math. Soc., Providence, RI, 2004.
  • [7] H. Hedenmalm, B. Korenblum, K. Zhu, Theory of Bergman spaces. Springer Verlag, New York, Inc., 2000.
  • [8] K. Zhu, Operator theory in function spaces. Mathematical Surveys and Monographs 138, Amer. Math. Soc., Providence, 2007.
  • [9] J. O. Bonyo, Groups of isometries associated with automorphisms of the half plane. Ph.D. dissertation, Mississippi State University, USA, 2015.
  • [10] S. Ballamoole, J. O. Bonyo, T. L. Miller, V. G. Miller, Ces`aro operators on the Hardy and Bergman spaces of the half plane. Complex Anal. Oper. Theory 10 (2016), 187–203. [11] K. Hoffman, Banach spaces of analytic functions. Prentice - Hall, Inc., Englewood Cliffs, N.J., 1962.

Reproducing Kernels for Hardy and Bergman Spaces of the Upper Half Plane

Year 2020, Volume: 3 Issue: 1, 13 - 23, 25.03.2020

Job Bonyo

https://doi.org/10.33434/cams.631112

Abstract

Using invertible isometries between Hardy and Bergman spaces of the unit disk $\D$ and the corresponding spaces of the upper half plane $\uP$, we determine explicitly the reproducing kernels for the Hardy and Bergman spaces of $\uP$. As a consequence, we obtain the duality relations for the reflexive Hardy and Bergman spaces of the half plane $\uP$.

Keywords

Reproducing kernel Hardy and Bergman spaces Bergman projection

References

  • [1] E. Albrecht, T. L. Miller, M. M. Neumann, Spectral properties of generalized Ces`aro operators on Hardy and weighted Bergman spaces. Arch. Math. (Basel), 85 (2005), 446–459.
  • [2] J. B. Garnett, Bounded Analytic Functions. Graduate Texts in Mathematics, Revised First Edition, Springer, Berlin, 2010.
  • [3] P. Duren, Theory of Hp spaces. Academic Press, New York, 1970.
  • [4] M. M. Peloso, Classical spaces of Holomorphic functions. Technical report, Universit di Milano, 2014.
  • [5] D. Bekolle, A.Bonimi. G. Garrigos, C. Nana, M. Peloso, F. Ricci, Lecture notes on Bergman projections in tube domais over cones: an analytic and geometric viewpoint, IMHOTEP J. Afr. Math. Pures Appl. 5 (2004). http://webs.um.es/gustavo.garrigos/papers/workshop5.pdf
  • [6] P. Duren, A. Schuster, Bergman spaces. Mathematical Surveys and Monographs 100, Amer. Math. Soc., Providence, RI, 2004.
  • [7] H. Hedenmalm, B. Korenblum, K. Zhu, Theory of Bergman spaces. Springer Verlag, New York, Inc., 2000.
  • [8] K. Zhu, Operator theory in function spaces. Mathematical Surveys and Monographs 138, Amer. Math. Soc., Providence, 2007.
  • [9] J. O. Bonyo, Groups of isometries associated with automorphisms of the half plane. Ph.D. dissertation, Mississippi State University, USA, 2015.
  • [10] S. Ballamoole, J. O. Bonyo, T. L. Miller, V. G. Miller, Ces`aro operators on the Hardy and Bergman spaces of the half plane. Complex Anal. Oper. Theory 10 (2016), 187–203. [11] K. Hoffman, Banach spaces of analytic functions. Prentice - Hall, Inc., Englewood Cliffs, N.J., 1962.
There are 10 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Job Bonyo 0000-0002-6442-4211

Publication Date March 25, 2020
Submission Date October 8, 2019
Acceptance Date February 13, 2020
Published in Issue Year 2020 Volume: 3 Issue: 1

Cite

APA Bonyo, J. (2020). Reproducing Kernels for Hardy and Bergman Spaces of the Upper Half Plane. Communications in Advanced Mathematical Sciences, 3(1), 13-23. https://doi.org/10.33434/cams.631112
AMA Bonyo J. Reproducing Kernels for Hardy and Bergman Spaces of the Upper Half Plane. Communications in Advanced Mathematical Sciences. March 2020;3(1):13-23. doi:10.33434/cams.631112
Chicago Bonyo, Job. “Reproducing Kernels for Hardy and Bergman Spaces of the Upper Half Plane”. Communications in Advanced Mathematical Sciences 3, no. 1 (March 2020): 13-23. https://doi.org/10.33434/cams.631112.
EndNote Bonyo J (March 1, 2020) Reproducing Kernels for Hardy and Bergman Spaces of the Upper Half Plane. Communications in Advanced Mathematical Sciences 3 1 13–23.
IEEE J. Bonyo, “Reproducing Kernels for Hardy and Bergman Spaces of the Upper Half Plane”, Communications in Advanced Mathematical Sciences, vol. 3, no. 1, pp. 13–23, 2020, doi: 10.33434/cams.631112.
ISNAD Bonyo, Job. “Reproducing Kernels for Hardy and Bergman Spaces of the Upper Half Plane”. Communications in Advanced Mathematical Sciences 3/1 (March 2020), 13-23. https://doi.org/10.33434/cams.631112.
JAMA Bonyo J. Reproducing Kernels for Hardy and Bergman Spaces of the Upper Half Plane. Communications in Advanced Mathematical Sciences. 2020;3:13–23.
MLA Bonyo, Job. “Reproducing Kernels for Hardy and Bergman Spaces of the Upper Half Plane”. Communications in Advanced Mathematical Sciences, vol. 3, no. 1, 2020, pp. 13-23, doi:10.33434/cams.631112.
Vancouver Bonyo J. Reproducing Kernels for Hardy and Bergman Spaces of the Upper Half Plane. Communications in Advanced Mathematical Sciences. 2020;3(1):13-2.
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