Skip to main content

Generalized Libera Operator on Mixed-Norm Spaces

  • Conference paper
  • First Online:
Proceedings of the Seventh International Conference on Mathematics and Computing

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 1412))

  • 569 Accesses

Abstract

In this paper, we discuss the boundedness of generalized Libera operator \(\varLambda ^{\gamma }\) on mixed-norm spaces \(H^{p,q}_{\alpha ,\nu }\). As a consequence, we find few results about the action of the operator \(\varLambda ^{\gamma }\) on various function spaces such as Hardy, Zygmund, Lipschitz, Bloch type, and Besov spaces.

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 189.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 249.99
Price excludes VAT (USA)
  • Compact, lightweight 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. Aulaskari R, Zhao R (1999) Boundedness and compactness properties of the Libera transform. Complex analysis and differential equations (Uppsala, 1997), vol 64 of Acta Universitatis Upsaliensis. Skrifter rörande Uppsala Universitet. C. Organisation och Historia. Uppsala University, Uppsala, Sweden, pp 69–80

    Google Scholar 

  2. Avetisyan K, Stević S (2009) The generalized Libera transform is bounded on the Besov mixed-norm, BMOA and VMOA spaces on the unit disc. Appl Math Comput 213(2):304–311

    MathSciNet  MATH  Google Scholar 

  3. Danikas N, Ruscheweyh S, Siskakis AG (1994) Metrical and topological properties of a generalized Libera transform. Arch Math 63(6):517–524

    Article  MathSciNet  Google Scholar 

  4. Libera RJ (1965) Some classes of regular univalent functions. Proc Amer Math Soc 16:755–758

    Article  MathSciNet  Google Scholar 

  5. Nowak M, Pavlović M (2010) On the Libera operator. J Math Anal Appl 370(2):588–599

    Article  MathSciNet  Google Scholar 

  6. Pavlović M, (2014) Definition and properties of the Libera operator on mixed norm spaces. Sci World J, Article ID 590656

    Google Scholar 

  7. Ruscheweyh S, Siskakis AG (2008) Corrigendum to: mertical and toplogical properties of a generalized Libera transform. Arch Math 91(3):254–255

    Article  MathSciNet  Google Scholar 

  8. Siskakis AG (1987) Composition semigroups and the Cesàro operator on \(H^p\). J Lond Math Soc 36(2):153–164

    Google Scholar 

  9. Siskakis AG (1987) Semigroups of composition operators in Bergman spaces. Bull Aust Math Soc 35(2):397–406

    Article  MathSciNet  Google Scholar 

  10. Xiao J (1997) Cesàro-type operators on Hardy, BMOA and Bloch spaces. Archiv der Mathematik 68(5):398–406

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Ethics declarations

We confirm that we have no potential conflict of interest.

Rights and permissions

Reprints and permissions

Copyright information

© 2022 The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Naik, S., Rajbangshi, K. (2022). Generalized Libera Operator on Mixed-Norm Spaces. In: Giri, D., Raymond Choo, KK., Ponnusamy, S., Meng, W., Akleylek, S., Prasad Maity, S. (eds) Proceedings of the Seventh International Conference on Mathematics and Computing . Advances in Intelligent Systems and Computing, vol 1412. Springer, Singapore. https://doi.org/10.1007/978-981-16-6890-6_61

Download citation

Publish with us

Policies and ethics