Skip to main content
SpringerLink
Log in

Bilinear Weighted Inequalities with Volterra Integral Operators

  • MATHEMATICS
  • Published:
Doklady Mathematics Aims and scope Submit manuscript

Abstract

Necessary and sufficient conditions for the boundedness of a class of bilinear inequalities with Volterra integral operators in weighted Lebesgue spaces on the real half-line are given.

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

Access this article

Log in via an institution

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. R. Oinarov, Proc. Steklov Inst. Math. 204, 205–214 (1994).

    Google Scholar 

  2. D. V. Prokhorov, V. D. Stepanov, and E. P. Ushakova, “Hardy–Steklov integral operators,” Modern Problems in Mathematics (Mat. Inst. Ross. Akad. Nauk, Moscow, 2016), Vol. 22, pp. 3–185 [in Russian].

    Google Scholar 

  3. M. I. A. Cañestro, P. O. Salvador, and C. R. Torreblanca, J. Math. Anal. Appl. 387 (1), 320–334 (2012).

    Article  MathSciNet  Google Scholar 

  4. M. Cwikel and R. Kerman, J. Funct. Anal. 106 (1), 130–144 (1992).

    Article  MathSciNet  Google Scholar 

  5. L. Grafakos and R. H. Torres, J. Funct. Anal. 187 (1), 1–24 (2001).

    Article  MathSciNet  Google Scholar 

  6. M. Křepela, Proc. Edinburgh Math. Soc. 60 (2), 955–971 (2017).

    Article  MathSciNet  Google Scholar 

  7. P. Jain, S. Kanjilal, V. D. Stepanov, and E. P. Ushakova, Math. Notes 104 (6), 823–832 (2018).

    Article  MathSciNet  Google Scholar 

  8. D. V. Prokhorov, Proc. Steklov Inst. Math. 293, 272–287 (2016).

    Article  MathSciNet  Google Scholar 

  9. M. Křepela, Publ. Mat. 61, 3–50 (2017).

    Article  MathSciNet  Google Scholar 

  10. V. D. Stepanov and G. E. Shambilova, Dokl. Math. 96 (3), 631–635 (2017).

    Article  MathSciNet  Google Scholar 

  11. V. D. Stepanov and G. E. Shambilova, Sib. Math. J. 59 (3), 505–522 (2018).

    Article  MathSciNet  Google Scholar 

  12. V. D. Stepanov and G. E. Shambilova, Dokl. Math. 94 (3), 697–702 (2016).

    Article  MathSciNet  Google Scholar 

  13. V. D. Stepanov and G. E. Shambilova, Dokl. Math. 96 (1), 315–320 (2017).

    Article  MathSciNet  Google Scholar 

  14. V. D. Stepanov and G. E. Shambilova, Sib. Math. J. 57 (5), 884–904 (2016).

    Article  MathSciNet  Google Scholar 

  15. V. D. Stepanov and G. E. Shambilova, Eurasian Math. J. 8 (2), 47–73 (2017).

    Google Scholar 

Download references

Funding

This work was supported in part by the Russian Foundation for Basic Research, project no. 19-01-00223. The study of the second author was performed in part within the RUDN University Program 5-100.

Author information

Authors and Affiliations

  1. Computing Center, Far East Branch, Russian Academy of Sciences, 680000, Khabarovsk, Russia

    V. D. Stepanov

  2. RUDN University, 117198, Moscow, Russia

    G. E. Shambilova

Authors
  1. V. D. Stepanov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. G. E. Shambilova
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to V. D. Stepanov.

Additional information

Translated by N. Berestova

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Stepanov, V.D., Shambilova, G.E. Bilinear Weighted Inequalities with Volterra Integral Operators. Dokl. Math. 99, 290–294 (2019). https://doi.org/10.1134/S1064562419030165

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1064562419030165

Search

Navigation