Skip to main content
SpringerLink
Log in

Weighted Norm Inequality for General One-Sided Vector Valued Maximal Function

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

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 1262))

Abstract

In this article, we study the one weight vector valued norm inequality for the general one-sided maximal function \(M_w^+\). We prove a sufficient, as well as a necessary condition for the weighted boundedness of the one-sided maximal function \(M_w^+\) in the vector valued setting. We establish an inequality for the operator \(M_w^+\) in the scalar setting similar to the Fefferman-Stein’s weighted lemma.

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 169.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
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. Muckenhoupt B (1972) Weighted norm inequalities for the Hardy maximal functions. Trans Am Math Soc 165:207–226

    Article  MathSciNet  Google Scholar 

  2. Anderson KF, John RT (1980/1981) Weighted inequalities for vector-valued maximal functions and singular integrals. Stud Math 69:19–31

    Google Scholar 

  3. Grafakos L (2008) Classical fourier analysis.: graduate texts in mathematics, vol 249, 2nd edn. Springer, Berlin

    Google Scholar 

  4. Sawyer E (1986) Weighted inequalities for the one-sided Hardy-Littlewood maximal functions. Trans Am Math Soc 297:53–61

    Article  MathSciNet  Google Scholar 

  5. Shrivastava S (2016) Weighted and vector-valued inequalities for one-sided maximal functions. Proc Indian Acad Sci (Math Sci) 126:359–380

    Google Scholar 

  6. Fefferman C, Stein EM (1971) Some maximal inequalities. Am J Math 93:107–115

    Article  MathSciNet  Google Scholar 

  7. Martin-Reyes FJ, Salvador PO, de La Torre A (1990) Weighted inequalities for one- sided maximal functions. Trans Am Math Soc 319:517–534

    Article  MathSciNet  Google Scholar 

  8. Qinsheng L (1996) A note on the weighted norm inequality for the one-sided maximal operator. Proc Am Math Soc 124:527–537

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

D. Chutia was supported by the DST INSPIRE (Grant No. DST/INSPIRE Fellowship/2017/IF170509). R. Haloi was supported by the DST MATRICS (Grant No. SERB/F/12082/2018-2019).

Author information

Authors and Affiliations

  1. Tezpur University, Tezpur, 784028, India

    Duranta Chutia & Rajib Haloi

Authors
  1. Duranta Chutia
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Rajib Haloi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Rajib Haloi .

Editor information

Editors and Affiliations

  1. Department of Information Technology, Maulana Abul Kalam Azad University of Technology, Haringhata, West Bengal, India

    Debasis Giri

  2. School of Computing and Information Systems, University of Melbourne, Melbourne, VIC, Australia

    Rajkumar Buyya

  3. Department of Mathematics, Indian Institute of Technology Madras, Chennai, India

    S. Ponnusamy

  4. Department of Computer Science and Engineering, Maulana Abul Kalam Azad University of Technology, Haringhata, West Bengal, India

    Debashis De

  5. Unconventional Computing Laboratory, Department of Computer Science and Creative Technologies, University of the West of England, Bristol, UK

    Andrew Adamatzky

  6. Faculty of Science, Engineering and Built Environment, Deakin University Geelong, Geelong, VIC, Australia

    Jemal H. Abawajy

Rights and permissions

Reprints and permissions

Copyright information

© 2021 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

Chutia, D., Haloi, R. (2021). Weighted Norm Inequality for General One-Sided Vector Valued Maximal Function. In: Giri, D., Buyya, R., Ponnusamy, S., De, D., Adamatzky, A., Abawajy, J.H. (eds) Proceedings of the Sixth International Conference on Mathematics and Computing. Advances in Intelligent Systems and Computing, vol 1262. Springer, Singapore. https://doi.org/10.1007/978-981-15-8061-1_45

Download citation

Publish with us

Policies and ethics

Search

Navigation