Skip to main content
SpringerLink
Log in

Integral Operators with Periodic Kernels in Spaces of Integrable Functions

  • Published:
Russian Mathematics Aims and scope Submit manuscript

Abstract

We consider integral operators with periodic kernels acting from Lp(ℝn) to Lq(ℝn). We obtain sufficient conditions for boundedness of that operators. Moreover we obtain compactness conditions for the product of the integral operator with periodic kernel and the operator of multiplication by an essentially bounded function.

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. Thieme, H.R. “Renewal theorems for some mathematical models in epidemiology”, J. Integral Equat. 8 (3), 185–216 (1985).

    MathSciNet  MATH  Google Scholar 

  2. Tsalyuk, Z.B. “Volterra integral equations”, Itogi nauki i techniki. Ser. matem. anal. 15, 131–198 (1977).

    MathSciNet  MATH  Google Scholar 

  3. Pulyaev, V.F. Development of theory of linear integral equations with periodic and almost periodic kernels, Diss. … doct. phys.-matem. nauk (S.-Peterb. gos. un-t, Sankt-Peterburg, 2001) [in Russian].

    Google Scholar 

  4. Barsukova, V.Yu., Pulyaev, V.F. “Asymptotics of solution of integral equation on half-axis with periodic kernel”, Izv. vuzov. Severo-Caucas. region. Estestv. nauki 4, 3–5 (2003).

    MATH  Google Scholar 

  5. Barsukova, V.Yu. Exponential and bounded solutions of linear integral equations with periodic kernels, Diss. … cand. phys.-matem. nauk (Rost. gos. un-t, Rostov-na-Donu, 2005) [in Russian].

    Google Scholar 

  6. Danford, N., Schwarz, J. Linear operators. General theory (IL, Moscow, 1962) [in Russian].

    Google Scholar 

  7. Avsyankin, O.G., Ulyanova, L.V. “On Boundedness and Compactness of the Multidimensional Integral Operators with Periodical Kernels”, Izv. vuzov. Severo-Caucas. region. Estestv. nauki 1, 5–8 (2014).

    Google Scholar 

  8. Karapetyants, N.K. “Analog of the Hörmander theorem for domains different of ℝn”, DAN USSR 293 (6), 1294–1297 (1987) [in Russian].

    Google Scholar 

  9. Karapetyants, N.K., Samko, S.G. Equations with involutive operators (Birkhäuser, Boston - Basel - Berlin, 2001).

    Book  Google Scholar 

  10. Avsyankin, O.G. “Compactness of Some Operators of Convolution Type in Generalized Morrey Spaces”, Math. Notes 104 (3), 331–338 (2018).

    Article  MathSciNet  Google Scholar 

Download references

Funding

The research is performed with support of Russian Foundation for Basic Researches, grant no. 18-01-00094-A.

Author information

Authors and Affiliations

  1. Southern Federal University, 8a Mil’chakova str., Rostov-on-Don, 344090, Russia

    O. G. Avsyankin

Authors
  1. O. G. Avsyankin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to O. G. Avsyankin.

Additional information

Russian Text © The Author(s), 2020, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2020, No. 2, pp. 3–9.

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Avsyankin, O.G. Integral Operators with Periodic Kernels in Spaces of Integrable Functions. Russ Math. 64, 1–7 (2020). https://doi.org/10.3103/S1066369X20020012

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.3103/S1066369X20020012

Keywords

Search

Navigation