Skip to main content
Log in

Estimates of derivatives in a mixed Lp-norm on a domain and an extension of functions

  • Published:
Mathematical notes of the Academy of Sciences of the USSR Aims and scope Submit manuscript

Abstract

We extend to the case of a mixed Lp-norm the estimates of derivatives that are well known for the ordinary Lp-norm.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

Literature cited

  1. O. V. Besov, “The extension of functions from L lp and W lp ,” Trudy Mat. Inst., Akad. Nauk SSSR,89, 5–17 (1967).

    Google Scholar 

  2. V. P. Il'in, “Integral representations of differentiable functions and their application to problems on the extension of functions of the classes W (l)p (G),” Sibirsk. Matem. Zh.,8, No. 3, 573–586 (1967).

    Google Scholar 

  3. O. V. Besov and V. P. Il'in, “A natural extension of a class of domains in embedding theorems,” Mat. Sb.,75, No. 4, 483–495 (1968).

    Google Scholar 

  4. O. V. Besov, “On coerciveness in a nonisotropic Sobolev space,” Mat. Sb.,73, No. 4, 585–599 (1967).

    Google Scholar 

  5. A. P. Calderon, “Lebesgue spaces of differentiable functions and distributions. Partial differential equations,” Proceedings of Symposia in Pure Mathematics (IV), 33–49 (1961).

  6. K. T. Smith, “Inequalities for formally positive integro-differential forms,” Bull. Amer. Math. Soc.,67, 368–370 (1961).

    Google Scholar 

  7. P. I. Lizorkin, “Multipliers of Fourier integrals and estimates for convolutions in spaces with a mixed norm. Applications,” Izv. Akad. Nauk SSSR, Ser. Matem.,34, No. 1, 218–247 (1970).

    Google Scholar 

  8. L. Hörmander, “Estimates for operators invariant under a translation” [Russian translation], Moscow (1962).

  9. A. Benedec, A. P. Calderon, and R. Panzone, “Convolution operators on Banach space valued functions,” Proc. Nat. Acad. Sci. USA,48, No. 3, 356–365 (1962).

    Google Scholar 

  10. B. F. Jones, “A class of singular integrals,” Amer. J. Math.,88, No. 2, 441–462 (1964).

    Google Scholar 

  11. M. P. Krée, “Sur les multiplicateurs dans FLP,” C. R. Acad. Sci. Paris,260, No. 7, 4400–4403 (1965).

    Google Scholar 

  12. A. Benedec and R. Panzone, “The spaces LP with mixed norm,” Duke Math. J.,28, No. 3, 301–324 (1961).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Translated from Matematicheskie Zametki. Vol. 7, No. 2, pp. 147–154, February, 1970.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Besov, O.V. Estimates of derivatives in a mixed Lp-norm on a domain and an extension of functions. Mathematical Notes of the Academy of Sciences of the USSR 7, 89–94 (1970). https://doi.org/10.1007/BF01093488

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01093488

Navigation