Skip to main content
Log in

Characterizations for General Besov-Type Space in Clifford Analysis

  • Published:
Advances in Applied Clifford Algebras Aims and scope Submit manuscript

Abstract

In this paper, we obtain some characterizations for general Besov-type spaces by employing certain power series satisfying certain growth conditions in lieu of the weight function in Clifford analysis. The obtained results extend and generalize the corresponding results which are given in [6, 23].

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. El-Sayed Ahmed A.: On weighted α-Besov spaces and α-Bloch spaces of quaternion-valued functions. Numerical Functional Analysis and Optimization 29(9-10), 1064–1081 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  2. El-Sayed Ahmed A.: Lacunary series in quaternion B p,q spaces. Complex variables and elliptic equations 54(7), 705–723 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  3. El-Sayed Ahmed A., Gürlebeck K., Reséndis L.F., Tovar L.M.: Characterizations for the Bloch space by B p,q spaces in Clifford analysis. Complex variables and elliptic equations 51(2), 119–136 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  4. El-Sayed Ahmed A., Omran S.: Weighted classes of quaternion-valued functions. Banach Journal of Mathematical Analysis 6(2), 180–191 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  5. R. Aulaskari and P. Lappan, Criteria for an analytic function to be Bloch and a harmonic or meromorphic function to be normal. Complex analysis and its applications, Pitman Research Notes in Math. 305 Longman Scientific and Technical Harlow (1994), 136–146.

  6. Aulaskari R., He Y., Zhao R.: On entire functions, Bloch and normal functions. Chin. Ann. Math., Ser. B 17(2), 139–148 (1996)

    MATH  MathSciNet  Google Scholar 

  7. Bernstein S.: Harmonic Q p spaces. Computational Methods and Function Theory 9(1), 285–304 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  8. Bernstein S., Gürlebeck K., Reséndis L.F., Tovar L.M.: Dirichlet and Hardy spaces of harmonic and monogenic functions. Z. Anal. Anwend. 24(4), 763–789 (2006)

    MATH  Google Scholar 

  9. F. Brackx, R. Delanghe and F. Sommen, Clifford analysis. Pitman Research Notes in Math. Boston, London, Melbourne, (1982).

  10. Cnops J., Delange R.: Möbius invariant spaces in the unit ball. Appl. Anal. 73(1-2), 45–64 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  11. K. Gürlebeck and A. El-Sayed Ahmed, Integral norms for hyperholomorphic Bloch functions in the unit ball of \({\mathbb{R}^3}\) ,. Proceedings of the 3rd International ISAAC Congress held in Freie Universtaet Berlin-Germany, August 20–25 (2001), Editors H.Begehr, R. Gilbert and M.W. Wong, Kluwer Academic Publishers, World Scientific New Jersey, London, Singapore, Hong Kong, Vol I (2003), 253–262.

  12. Gürlebeck K., Kähler U., Shapiro M., Tovar L.M.: On Q p spaces of quaternion-valued functions. Journal of Complex Variables 39, 115–135 (1999)

    Article  MATH  Google Scholar 

  13. K. Gürlebeck, K. Habetha and W. W. Sprößig, Holomorphic functions in the plane and n-dimensional space. Basel: Birkhüser. xiii (2008).

  14. Gürlebeck K., Malonek H.R.: On strict inclusions of weighted Dirichlet spaces of monogenic functions. Bull. Austral. Math. Soc. 64, 33–50 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  15. Gürlebeck K., Sprößig W.: Quaternionic and Clifford calculus for Engineers and Physicists. John Wiley &. Sons, Chichester (1997)

    MATH  Google Scholar 

  16. He Z.H., Cao G.: Generalized integration operators between Bloch-type spaces and F(p, q, s) spaces. Taiwanese J. Math. 17(4), 1211–1225 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  17. Y. Liu and Y. Yu, The multiplication operator from F(p, q, s) spaces to nth weighted-type spaces on the unit disk. J. Funct. Spaces Appl. Article ID 343194 (2012).

  18. Liang Yu-Xia., Zhou Ze-Hua., Chen Ren-Yu.: Product of extended Cesro operator and composition operator from the logarithmic Bloch-type space to F(p, q, s) space on the unit ball. J. Comput. Anal. Appl. 15(3), 432–440 (2013)

    MATH  MathSciNet  Google Scholar 

  19. J. Rättyä, On some Complex function spaces and classes. Annales Academiae Scientiarum Fennicae. Series A I. Mathematica. Dissertationes. 124. Helsinki: Suomalainen Tiedeakatemia, (2001), 1–73.

  20. L. F. Reséndis and L. M. Tovar, Besov-type characterizations for Quaternionic Bloch functions. In: Le Hung Son et al (Eds) finite or infinite complex Analysis and its applications, Adv. Complex Analysis and applications, (Boston MA: Kluwer Academic Publishers) (2004), 207–220.

  21. Stroethoff K.: Besov-type characterizations for the Bloch space. Bull. Austral. Math. Soc. 39, 405–420 (1989)

    Article  MATH  MathSciNet  Google Scholar 

  22. Sudbery A.: Quaternionic analysis. Math. Proc. Cambridge Philos. Soc. 85, 199–225 (1979)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  23. R. Zhao, On a general family of function spaces, Annales Academiae Scientiarum Fennicae. Series A I. Mathematica. Dissertationes. 105. Helsinki: Suomalainen Tiedeakatemia, (1996), 1–56.

  24. Zhang X., He C., Cao F.: The equivalent norms of F(p, q, s) space in C n. J. Math. Anal. Appl. 401(2), 601–610 (2013)

    Article  ADS  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to A. El-Sayed Ahmed.

Additional information

This work is dedicated to Professor Klaus Gürlebeck on the occasion of his 60th birthday.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

El-Sayed Ahmed, A. Characterizations for General Besov-Type Space in Clifford Analysis. Adv. Appl. Clifford Algebras 24, 1011–1025 (2014). https://doi.org/10.1007/s00006-014-0477-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00006-014-0477-x

Keywords

Navigation