Bp,q-Functions and their Harmonic Majorants

  • S. Bernstein
  • K. Gürlebeck
  • L. F. Reséndis
  • Luis M. Tovar S.
Part of the Trends in Mathematics book series (TM)


The aim of this work is to characterize hyperholomorphic B p,q -functions in terms of harmonic majorants. In addition we point out how some important relations between B p,q , Bloch and Q p -spaces can be expressed in terms of their corresponding harmonic majorants.


Hyperholomorphic Bp,q-functions harmonic majorants 

Mathematics Subject Classification (2000)

Primary 30G35 Secondary 31B05 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    A. El-Sayed Ahmed, K. Gürlebeck, L.F. Resendis, L.M. Tovar, Characterizations for B p,q spaces by Bloch spaces in Clifford analysis, preprint Bauhaus Univ. Weimar, Germany 2002.Google Scholar
  2. [2]
    R. Aulaskari and P. Lappan, Criteria for an analytic function in the Bloch space and harmonic or meromorphic function to be normal, Complex analysis and its application, Pitman Research Notes in Math. 305, Longman Scientific of Technical, Harlow, (1994), 136–146.Google Scholar
  3. [3]
    R. Aulaskari, L.F. Resendis, L.M. Tovar, Qp-spaces and Harmonic majorants, to appear in Complex Variables. Google Scholar
  4. [4]
    S. Axler, P. Bourlau, W. Raney, Harmonic Function Theory, Grad. Text in Math., Vol. 137, Springer Verlag, 2001.Google Scholar
  5. [5]
    J. Cnops and R. Delanghe, Möbius invariant spaces in the unit ball, Appl. Anal. 73 (2000), 45–64.MathSciNetCrossRefGoogle Scholar
  6. [6]
    R. Dautray, J. L. Lions, Mathematical analysis and numerical methods for Science and Technology, Vol. 1, Springer Verlag, 1990.CrossRefGoogle Scholar
  7. [7]
    K. Gürlebeck and A. El-Sayed Ahmed, Integral norms for hyperholomorphic Bloch-functions in the unit ball of R3, in: Progress in Analysis, Proceedings of the 3rd International ISAAC Congress, Volume I, Editors H. Begehr, R. Gilbert, M.W. Wong, World Scientific, New Jersey, London, Singapore, Hong Kong, 2003Google Scholar
  8. [8]
    K. Gürlebeck and A. El-Sayed Ahmed, On B q spaces of hyperholomorphic functions and the Bloch space in R3, in: Finite or Infinite Dimensional Complex Analysis and Applications, Le Hung Son (Ed.), W. Tutschke (Ed.), C.-C. Yang (Ed.), Advances in Complex Analysis and its Applications — 2, Kluwer Boston, 2003Google Scholar
  9. [9]
    K. Gürlebeck and H. R. Malonek, On strict inclusions of weighted Dirichlet spaces of monogenic functions, Bull. Austral. Math. Soc. 64 (2001), 33–50.MathSciNetCrossRefzbMATHGoogle Scholar
  10. [10]
    K. Gürlebeck, U. Kähler, M. Shapiro, L.M. Tovar, On Qp-spaces of quaternion-valued functions, Complex Variables 39 (1999), 115–135.CrossRefzbMATHGoogle Scholar
  11. [11]
    S. Kobayashi, Range sets and BMO norms of analytic functions, Canadian S. Math. XXXVI, No. 4 (1984), 747–755.CrossRefGoogle Scholar
  12. [12]
    I.M. Mitelman and M.V. Shapiro, Differentiation of the Martinelli-Bochner Integrals and the Notion of Hyperderivability, Math. Nachr. 172 (1995), 211–238.MathSciNetCrossRefzbMATHGoogle Scholar
  13. [13]
    L. F. Reséndis and L. M. Tovar, Besov-type Characterizations for Quaternionic Bloch Functions, in: Finite or Infinite Dimensional Complex Analysis and Applications, Le Hung Son (Ed.), W. Tutschke (Ed.), C.-C. Yang (Ed.), Advances in complex analysis and its applications — 2, Kluwer Boston, 2003Google Scholar
  14. [14]
    A. Sudbery, Quaternionic analysis, Math. Proc. Cambridge Philos. Soc. 85 (1979), 199–225.MathSciNetCrossRefzbMATHGoogle Scholar
  15. [15]
    K. Stroethoff, Besov-type characterizations for the Bloch space, Bull. Austral. Math. Soc. 39 (1989), 405–420.MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer Basel AG 2004

Authors and Affiliations

  • S. Bernstein
    • 1
  • K. Gürlebeck
    • 1
  • L. F. Reséndis
    • 2
  • Luis M. Tovar S.
    • 3
  1. 1.Institut für Mathematik und PhysikBauhaus-Universität WeimarWeimarGermany
  2. 2.Universidad Autónoma MetropolitanaUnidad Azcapotzalco C.B.I.Mexico
  3. 3.Escuela Superior de Física y Matemáticas del IPN Edif. 9 Unidad ALMZacatenco del IPND.F. MéxicoMexico

Personalised recommendations