On Bloch hyperharmonic functions



Abstract

In this note we give necessary and sufficient conditions for a hyperharmonic function to be a Bloch function.


Keywords

hyperharmonic function; HL-property,; Möbius automorphism; Laplace-Beltrami operator

1. L. Ahlfors, Möbius transformations in several dimensions, University of Minesota, School of Mathematics (1981).
2. J.M. Anderson, J.G. Clunie, C.H. Pommerenki, On Bloch functions and normal functions, J. Reine Angew. Math. 270 (1974), 12-37.
3. S. Axler, The Bergman space, the Bloch space, and commutators of multiplication operators, Duke Math. J. 53 (1986), 315-332.
4. S. Axler, P. Bourdon, W. Ramey, Harmonic function theory, Springer-Verlag, New York 1992.
5. F. Beatrous, J. Burbea, Holomorphic Sobolev spaces on the ball, Dissertationes Math. 256 (1986), 315-332.
6. R.R. Coifman, R. Rochberg, G. Weiss, Factorization theorems for Hardy spaces in several complex variables, Ann. of Math. 103 (1976), 611-635.
7. C. Fefferman, E.M. Stein, H^p spaces of several variables, Acta Math. 129 (1972), 137-193.
8. G.H. Hardy, J.E. Littlewood, Some properties of conjugate function, J. Reine. Angew. Math. 167 (1931), 405-423.
9. U. Kuran, Subharmonic behaviour of |h|^p (p>0, h harmonic), J. London Math. Soc. 8 (1974), 529-538.
10. K. Muramoto, Harmonic Bloch and BMO functions on the unit ball in several variables, Tokyo J. Math. 11, 2 (1988), 381-386.
11. M. Nowak, Bloch space on the unit ball of C^n, Ann. Acad. Sci. Fenn. Math. 23 (1998), 461-473.
12. C. Ouyang, W. Weisheng, R. Zhao, Characterizations of Bergman spaces and Bloch space in the unit ball of C^n, Trans. Amer. Math. Soc. 347 (1995), 4301-4313.
13. M. Pavlović, On subharmonic behaviour of functions on balls in R^n, Publ. Inst. Math. (Belgrade), 55 (1994), 18-22.
14. M. Pavlović, Subharmonic behaviour of smooth functions, Mat. Vesnik 48, no. 1-2 (1996), 15-21.
15. S. Stević, An equivalent norm on BMO spaces, Acta Sci. Math. 66 (2000), 553-563.
16. S. Stević, On eigenfunctions of the Laplace operator on a bounded domain, Sci. Ser. A Math. Sci. (N.S.) 7 (2001), 51-55.
17. S. Stević, On subharmonic behaviour of functions in C^n, (to appear).
18. R.M. Timoney, Bloch functions in several complex variables, Bull. London Math. Soc. 12 (1980), 241-267.
Download

Published : 2003-01-30


StevićS. (2003). On Bloch hyperharmonic functions. Annales Mathematicae Silesianae, 16, 57-64. Retrieved from https://www.journals.us.edu.pl/index.php/AMSIL/article/view/14108

Stevo Stević  sstevic@ptt.yu
Matematički Fakultet, Serbia, Yugoslavia  Serbia



The Copyright Holders of the submitted text are the Author and the Journal. The Reader is granted the right to use the pdf documents under the provisions of the Creative Commons 4.0 International License: Attribution (CC BY). The user can copy and redistribute the material in any medium or format and remix, transform, and build upon the material for any purpose.

  1. License
    This journal provides immediate open access to its content under the Creative Commons BY 4.0 license (http://creativecommons.org/licenses/by/4.0/). Authors who publish with this journal retain all copyrights and agree to the terms of the above-mentioned CC BY 4.0 license.
  2. Author’s Warranties
    The author warrants that the article is original, written by stated author/s, has not been published before, contains no unlawful statements, does not infringe the rights of others, is subject to copyright that is vested exclusively in the author and free of any third party rights, and that any necessary written permissions to quote from other sources have been obtained by the author/s.
  3. User Rights
    Under the Creative Commons Attribution license, the users are free to share (copy, distribute and transmit the contribution) and adapt (remix, transform, and build upon the material) the article for any purpose, provided they attribute the contribution in the manner specified by the author or licensor.
  4. Co-Authorship
    If the article was prepared jointly with other authors, the signatory of this form warrants that he/she has been authorized by all co-authors to sign this agreement on their behalf, and agrees to inform his/her co-authors of the terms of this agreement.