Skip to main content
SpringerLink
Log in

An exact estimate of the boundary behavior of functions from hardy-sobolev classes in the critical case

  • Published:
Mathematical Notes Aims and scope Submit manuscript

Abstract

In the critical case αp=n functions from the Hardy-Sobolev spacesH pα (B n) have a limit almost everywhere on the boundary along certain regions of exponential contact with the boundary. It is proved in the paper that the maximal operator associated with these regions is bounded as an operator fromH pα (B n) toL p(ϖB n).

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. W. Rudin,Function Theory in the Unit Ball of ℂn, Springer-Verlag, Heidelberg-Berlin-New York (1981).

    Google Scholar 

  2. P. Ahern and W. Cohn, “Exceptional sets for Hardy-Sobolev functions”,Indiana Univ. Math. J.,38, No. 2, 417–452 (1989).

    MathSciNet  Google Scholar 

  3. V. G. Krotov, “Estimates for maximal operators involving boundary behavior and their applications”,Trudy Mat. Inst. Steklov [Proc. Steklov Inst. Math.],190, 117–138 (1989).

    MATH  MathSciNet  Google Scholar 

  4. A. Nagel, W. Rudin, and J. Shapiro, “Tangential boundary behavior of functions in Dirichlet-type spaces”,Ann. Math.,116, No. 2, 331–360 (1982).

    MathSciNet  Google Scholar 

  5. V. G. Krotov, “Boundary behavior of fractional integrals of holomorphic functions in the unit ball in ℂn”,Izv. Vyssh. Uchebn. Zaved. Mat. [Soviet Math. (Iz. VUZ)], No. 4, 73–75 (1988).

    MATH  MathSciNet  Google Scholar 

  6. J. Sueiro, “Tangential boundary limits and exceptional sets for holomorphic functions in Dirichlet-type spaces”,Math. Ann.,286, No. 4, 661–678 (1990).

    MATH  MathSciNet  Google Scholar 

  7. F. Beatrous, “Boundary continuity of holomorphic Sobolev function in the ball”,Proc. Amer. Math. Soc.,97, No. 1, 29–41 (1986).

    MATH  MathSciNet  Google Scholar 

  8. V. G. Krotov, “Exact estimation of the boundary behavior of functions from the Hardy-Sobolev classesH pα in the critical case αp=n”,Dokl. Akad. Nauk SSSR [Soviet Math. Dokl.],319, No. 1, 42–45 (1991).

    MATH  Google Scholar 

  9. P. M. Volnyakov,Estimates of the Fatoux Property for Functions from the Hardy-Sobolev Classes [in Russian], Kandidat thesis in the physico-mathematical sciences, Odessa State Univ., Odessa (1992).

    Google Scholar 

  10. V. G. Krotov, “Boundary behavior of functions in Hardy-Sobolev spaces”,Izv. Akad. Nauk SSSR Ser. Mat. [Math. USSR-Izv.],54, No. 1, 957–974 (1990).

    MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Belorussian State Polytechnic Academy, Minsk

    V. G. Krotov

Authors
  1. V. G. Krotov
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated fromMatematicheskie Zametki, Vol. 62, No. 4, pp. 527–539, October, 1997.

Translated by N. K. Kulman

Rights and permissions

Reprints and permissions

About this article

Cite this article

Krotov, V.G. An exact estimate of the boundary behavior of functions from hardy-sobolev classes in the critical case. Math Notes 62, 439–448 (1997). https://doi.org/10.1007/BF02358977

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02358977

Key words

Search

Navigation