Skip to main content

\(\mathcal{Q}_{K}\) Spaces via Other Derivatives

  • Chapter
  • First Online:
Mobius Invariant QK Spaces
  • 457 Accesses

Abstract

In this chapter we characterize \(\mathcal{Q}_{K}\) spaces in terms of higher order derivatives and fractional derivatives. We also provide a derivative-free characterization for \(\mathcal{Q}_{K}\) spaces. Each characterization depends on either condition (3.1) or condition (3.3) for some σ > 0.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 89.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 119.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 119.99
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

References

  1. S. Axler, The Bergman spaces, the Bloch space, and commutators of multiplication operators. Duke Math. J. 53, 315–332 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  2. M. Essén, H. Wulan, J. Xiao, Function-theoretic aspects of Möbius invariant \(\mathcal{Q}_{K}\) spaces. J. Funct. Anal. 230, 78–115 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  3. H. Hedenmalm, B. Korenblum, K. Zhu, Theory of Bergman Spaces (Springer, New York, 2000)

    Book  MATH  Google Scholar 

  4. H. Wulan, K. Zhu, \(\mathcal{Q}_{K}\) spaces via higher order derivatives. Rocky Mt. J. Math. 38, 329–350 (2008)

    Google Scholar 

  5. H. Wulan, K. Zhu, Derivative free characterizations of \(\mathcal{Q}_{K}\) spaces. J. Aust. Math. Soc. 82, 283–295 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  6. H. Wulan, J. Zhou, \(\mathcal{Q}_{K}\) and Morrey type spaces. Ann. Acad. Sci. Fenn. Math. 38, 193–207 (2013)

    Google Scholar 

  7. K. Zhu, Operator Theory in Function Spaces, 2nd edn. (American Mathematical Society, Providence, 2007)

    Book  MATH  Google Scholar 

  8. K. Zhu, Schatten class Hankel operators on the Bergman space of the unit ball. Am. J. Math. 113, 147–167 (1991)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG

About this chapter

Cite this chapter

Wulan, H., Zhu, K. (2017). \(\mathcal{Q}_{K}\) Spaces via Other Derivatives. In: Mobius Invariant QK Spaces. Springer, Cham. https://doi.org/10.1007/978-3-319-58287-0_5

Download citation

Publish with us

Policies and ethics