Skip to main content
SpringerLink
Log in

Fractional integrals of periodic functions of several variables

  • Published:
Approximation Theory and its Applications

Abstract

In this paper it has been systematically studied the imbedding properties of fractional integral operators of periodic functions of several variables, and isomorphic properties of fractional integral operators in the spaces of Lipschitz continuous functions. It has also been proved that the space of fractional integration, the space of Lipschitz continuous functions and the Sobolev space are identical in L2-norm. Results obtained here are not true for fractional integrals (or Riesz potentials) in ℝn.

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. Cheng Minde & Chen Yungho, Fractional Integrals of Periodic Functions of Several Variables and the Approximation by Trigonometrical Polynomials, J. Beijing Univ., 1957, 3: 259–282.

    Google Scholar 

  2. —, A Supplement to the Properties of Fractional Integral for Periodic Functions of Several Variables, J. Beijing Univ., 1959, 1: 15–29.

    Google Scholar 

  3. Wainger, S., Special Trigonometric Series in k-Dimensions, Memoirs A.M.S., 1965,59.

  4. Cheng Minde & Deng Donggao, Fractional Integration of Periodic Functions of Several Variables in LP Space, Ke Xue Tong Bao (in Chinese), 24 (1979), 18: 817–820.

    Google Scholar 

  5. Cheng Minde, Fractional Integral Operators, Aug., 1986, ICM.

  6. Stein, E.M. Singular Integrals and Differentiability Properties of Functions, Princeton Univ. Press, Princeton, 1971.

    Google Scholar 

  7. Wang Kunyang, Approximation for Continuous Periodic Functions of Several Variables and Its Conjugate Function by Riesz Means on Set of Total Measure, Appr. Theory & Appl., 1 (1985), 4:19–55.

    Google Scholar 

  8. Lorentz, G.G., Approximation of Functions, New York, 1966.

  9. Adams, R.A., Sobolev Space, Academic Press, New York, 1975.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Mathematics Section Dept. of Basic Courses, Zhejiang Institute of Technology, 310014, Hangzhou, P.R. China

    Wang Shiming

Authors
  1. Wang Shiming
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Supported by NNSFC

Rights and permissions

Reprints and permissions

About this article

Cite this article

Shiming, W. Fractional integrals of periodic functions of several variables. Approx. Theory & its Appl. 9, 82–96 (1993). https://doi.org/10.1007/BF02836153

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02836153

Keywords

Search

Navigation