Skip to main content
SpringerLink
Log in

Note on Characterizations of the Harmonic Bergman Space

  • Conference paper
  • First Online:
Spectral Theory, Mathematical System Theory, Evolution Equations, Differential and Difference Equations

Part of the book series: Operator Theory: Advances and Applications ((OT,volume 221))

Abstract

In this paper, we solve the problem which was stated in [6].A ctually we obtain a characterization of harmonic Bergman space in terms of Lipschitz type condition with pseudo-hyperbolic metric on the unit ball in R n.

Mathematics Subject Classification (2000). Primary 31B05; Secondary 46E30.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. S. Axler, P. Bourdon and W. Ramey, Harmonic function theory, Springer-Verlag, New York, 1992.

    MATH  Google Scholar 

  2. B.R. Choe, H. Koo and Y.J. Lee, Positive Schatten(-Herz) class Toeplitz operators on the ball, Studia Math, 189 (2008), No. 1, 65-90.

    Article  MathSciNet  MATH  Google Scholar 

  3. B.R. Choe and Y.J. Lee, Note on atomic decompositions of harmonic Bergman functions, Proceedings of the 15th ICFIDCAA; Complex Analysis and its Applications, Osaka Municipal Universities Press, OCAMI Studies Series 2 (2007), 11-24.

    MathSciNet  Google Scholar 

  4. E.S. Choi and K. Na, Characterizations of the harmonic Bergman space on the ball, J. Math. Anal. Appl. 353 (2009), 375-385.

    Article  MathSciNet  MATH  Google Scholar 

  5. B.R. Choe, H. Koo and H. Yi, Derivatives of harmonic Bergman and Bloch functions on the ball, J. Math. Anal. Appl. 260 (2001), 100-123.

    Article  MathSciNet  MATH  Google Scholar 

  6. K. Nam, K. Na and E.S. Choi, Corrigendum of "Characterizations of the harmonic Bergman space on the ball" [J. Math. Anal. Appl. 353 (2009), 375-385], in press.

    Article  MathSciNet  Google Scholar 

  7. H. Wulan and K. Zhu, Lipschitz type characterizations for Bergman spaces, to appear in Canadian Math. Bull.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematical Sciences BK21-Mathematical Sciences Division, Seoul National University, Seoul, 151-742, Republic of Korea

    Kyesook Nam

  2. General Education, Mathematics, Hanshin University, Osan, Gyeonggi, 447-791, Republic of Korea

    Kyunguk Na

  3. Department of Mathematics, Korea University, Seoul, 136-701, Republic of Korea

    Eun Sun Choi

Authors
  1. Kyesook Nam
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Kyunguk Na
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Eun Sun Choi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Kyesook Nam .

Editor information

Editors and Affiliations

  1. , Abt. Mathematik V, Universität Ulm, Ulm, 89069, Germany

    Wolfgang Arendt

  2. Department of Mathematics, Virginia Polytechnic Institute, McBryde Hall 524, Blacksburg, 24061, Virginia, USA

    Joseph A. Ball

  3. Institut fĂĽr Mathematik, AG Modellierung, Numerik und, TU Berlin, StraĂźe des 17 Juni 136, Berlin, 10623, Berlin, Germany

    Jussi Behrndt

  4. Fak. II Mathematik & Naturwissenschaften, Institut fĂĽr Mathematik, TU Berlin, StraĂźe des 17. Juni 136, Berlin, 10623, Berlin, Germany

    Karl-Heinz Förster

  5. Fak. II Mathematik & Naturwissenschaften, Institut fĂĽr Mathematik, TU Berlin, StraĂźe des 17. Juni 136, Berlin, 10623, Berlin, Germany

    Volker Mehrmann

  6. , Institut fĂĽr Mathematik, TU Ilmenau, Weimarer Str. 25, Ilmenau, 98693, ThĂĽringen, Germany

    Carsten Trunk

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer Basel

About this paper

Cite this paper

Nam, K., Na, K., Choi, E.S. (2012). Note on Characterizations of the Harmonic Bergman Space. In: Arendt, W., Ball, J., Behrndt, J., Förster, KH., Mehrmann, V., Trunk, C. (eds) Spectral Theory, Mathematical System Theory, Evolution Equations, Differential and Difference Equations. Operator Theory: Advances and Applications, vol 221. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0297-0_29

Download citation

Publish with us

Policies and ethics

Search

Navigation