Complex Analysis and Operator Theory

, Volume 13, Issue 3, pp 901–914 | Cite as

The Harmonic Dirichlet–Besov Space and the Optimal Norm for the Bergman Projection

  • Djordjije VujadinovićEmail author


We found the optimal operator-norm constant for the harmonic Bergman projection in the context of harmonic Dirichlet–Besov space regarding the natural semi-norm defined on it. Also, we give the two-side norm estimation when it comes to the complete norm.


Harmonic Besov space Harmonic Bergman projection Zonal harmonics Bochner spaces 

Mathematics Subject Classification

Primary 46E20 46E22 


  1. 1.
    Axler, S., Bourdon, P., Ramey, W.: Harmonic Function Theory. Springer, New York (2000)zbMATHGoogle Scholar
  2. 2.
    Choe, B.R., Koo, H., Lee, H.J.: Positive Schatten class Toeplitz operators on the ball. Studia Math. 189(1), 65–90 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Choe, B.R., Koo, H., Nam, K.: Optimal norm estimate of operators related to the harmonic Bergman projection on the ball. Tohoku Math. J. 62, 357–374 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Dragomir, S.S., Agarwal, R.P., Barnett, N.S.: Inequalities for Beta and Gamma functions via some classical and new integral inequalities. J. Inequal. Appl. 5(2), 103–165 (2000)MathSciNetzbMATHGoogle Scholar
  5. 5.
    Gergün, S., Kaptanoğlu, H.T., Üreyen, A.E.: Harmonic Besov spaces on the ball. Int. J. Math. 27(9), 1650070 (2016)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Jevtić, M., Pavlović, M.: Harmonic Besov space on the unit ball in \(\mathbf{R}^{n}\). Rocky Mount. J. Math. 31(3), 1305–1316 (2001)CrossRefzbMATHGoogle Scholar
  7. 7.
    Jevtić, M., Pavlović, M.: Harmonic Bergman functions on the unit ball in \(\mathbf{R}^{n}\). Acta Math. Hung. 85(1–2), 91–96 (1999)Google Scholar
  8. 8.
    Vujadinović, Dj: Some estimates for the norm of the Bergman projection on Besov spaces. Integr. Equ. Oper. Theory 76, 213–224 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Vujadinović, Dj.: The norm of the Harmonic Bergman Projection and Besov space. arxiv:1709.04335

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Faculty of MathematicsUniversity of MontenegroPodgoricaMontenegro

Personalised recommendations