Skip to main content
Log in

Inner functions in \(W_{\alpha }\) as improving multipliers

  • Original Paper
  • Published:
Annals of Functional Analysis Aims and scope Submit manuscript

Abstract

In this article, we give some characterizations of the inner functions in the space of \(W_{\alpha }\). Meanwhile, the zero sets in \(W_{\alpha }\) are also studied.

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.

Institutional subscriptions

Similar content being viewed by others

References

  1. Blasi, D., Pau, J.: A characterization of Besov-type spaces and applications to Hankel-type operators. Michigan Math. J. 56, 401–417 (2008)

    Article  MathSciNet  Google Scholar 

  2. Dyakonov, K.M.: Division and multiplication by inner functions and embedding theorems for star-invariant subspaces. Am. J. Math. 115, 881–902 (1993)

    Article  MathSciNet  Google Scholar 

  3. Dyakonov, K.M.: Smooth functions and coinvariant subspaces of the shift operator. St. Petersburg Math. J. 4, 933–959 (1993)

    MathSciNet  Google Scholar 

  4. Dyakonov, K.M.: Besov spaces and outer functions. Michigan Math. J. 45, 143–157 (1998)

    Article  MathSciNet  Google Scholar 

  5. Dyakonov, K.M.: Holomorphic functions and quasiconformal mappings with smooth moduli. Adv. Math. 187, 146–172 (2004)

    Article  MathSciNet  Google Scholar 

  6. Dyakonov, K.M.: Self-improving behaviour of inner functions as multipliers. J. Funct. Anal. 240, 429–444 (2006)

    Article  MathSciNet  Google Scholar 

  7. Dyakonov, K.M., Girela, D.: On \(Q_p\) spaces and pseudoanalytic extension. Ann. Acad. Sci. Fenn. Ser. A Math. 25, 477–486 (2000)

    MATH  Google Scholar 

  8. Marshall, D.E., Sundberg, C.: Interpolating sequences for the multipliers of the Dirichlet space, manuscript (1994)

  9. McDonald, G., Sundberg, C.: Toeplitz operators on the disc. Indiana Univ. J. Math. 28, 595–611 (1979)

    Article  MathSciNet  Google Scholar 

  10. Pau, J., Pelez, J.: On the zeros of functions in Dirichlet-type spaces. Trans. Am. Math. Soc. 363, 1981–2002 (2011)

    Article  MathSciNet  Google Scholar 

  11. Pelez, J.: Inner functions as improving multipliers. J. Funct. Anal. 255, 1403–1418 (2008)

    Article  MathSciNet  Google Scholar 

  12. Rochberg, R., Wu, Z.: A new characterization of Dirichlet type spaces and applications. Ill. J. Math. 37, 101–122 (1993)

    Article  MathSciNet  Google Scholar 

  13. Shapiro, H.S., Shields, A.L.: On the zeros of functions with finite Dirichlet integral and some related function spaces. Math. Z. 80, 217–229 (1962)

    Article  MathSciNet  Google Scholar 

  14. Wu, Z.: The predual and second predual of Wa. J. Fund. Anal. 116, 314–334 (1993)

    Article  Google Scholar 

  15. Wu, Z.: Carleson measures and multipliers for Dirichlet spaces. J. Funct. Anal. 169, 148–163 (1999)

    Article  MathSciNet  Google Scholar 

  16. Xiao, J.: Holomorphic \({\cal{Q}}\) classes. Lecture notes in mathematics 1767. Springer, Berlin (2001)

    Book  Google Scholar 

  17. Xiao, J.: Geometric \({\cal{Q}}\) functions. Birkhäuser, Basel (2006)

    Google Scholar 

  18. Zhao, R.: Distances from Bloch functions to some Möbius invariant spaces. Ann. Acad. Sci. Fenn. Math. 33, 303–313 (2008)

    MathSciNet  MATH  Google Scholar 

  19. Zhu, K.: Operator theory in function spaces. Marcel Dekker, New York (1990)

    MATH  Google Scholar 

  20. Zhu, K.: Operator theory in function spaces. American Mathematical Society, Providence (2007)

    Book  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Liu Yang.

Additional information

Communicated by Klaus Gürlebeck.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Du, J., Yang, L. Inner functions in \(W_{\alpha }\) as improving multipliers. Ann. Funct. Anal. 11, 555–566 (2020). https://doi.org/10.1007/s43034-019-00037-w

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s43034-019-00037-w

Keywords

Mathematics Subject Classification

Navigation