Skip to main content
SpringerLink
Log in

Embedding theorems for Bergman spaces in quasiconformal balls

  • Published:
manuscripta mathematica Aims and scope Submit manuscript

Abstract

The authors prove some embedding theorems for Bergman type spaces of functions defined on quasiconformal balls inR n,n≥2.

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

  • [FS] Fefferman, C. and E.M. Stein:H p-spaces of several variables.—Acta Math. 129 (1972). 137–193

    Article  MATH  MathSciNet  Google Scholar 

  • [GA] Garnett, J.B.: Bounded analytic functions.—Academic Press, 1981

  • [G] Gehring, F.W.: Characteristic properties of quasidisks.—Les Presses de l’Université de Montreal, Montreal, 1982

    MATH  Google Scholar 

  • [H] Hastings, W.W.: A Carleson measure theorem for Bergman, spaces.—Proc. Amer. Math. Soc. 52 (1975) 237–241

    Article  MATH  MathSciNet  Google Scholar 

  • [IN] Iwaniec, T. and C.A. Nolder: Hardy-Littlewood inequality for quasiregular mappings in certain domains inR n.—Ann. Acad. Sci. Fenn. Ser. AI10 (1985), 267–282

    MATH  MathSciNet  Google Scholar 

  • [J] Jones, P.W.: Extension theorems for BMO.—Indiana Univ. Math. J. 29 (1980), 41–66

    Article  MATH  MathSciNet  Google Scholar 

  • [K] Kuran, Ü: Subharmonic, behavior of |h|p (p>0, h harmonic function). —J. London Math. Soc. 8 (1974), 529–538

    Article  MATH  MathSciNet  Google Scholar 

  • [L] Lindenstauss, J. and L. Tzafriri: Classical Banach spaces II. Function spaces.-Springer-Verlag, 1979

  • [L1] Luecking, D.: Equivalent norms onL p-spaces of harmonic functions.— Monatshefte für Math. 96 (1983), 133–141

    Article  MATH  MathSciNet  Google Scholar 

  • [L2] Luecking, D.: Multipliers of Bergman spaces into Lebesgue spaces.— Proc. Edinburgh Math. Soc. 29 (1986), 125–131

    Article  MATH  MathSciNet  Google Scholar 

  • [MV] Mattila, P. and M. Vuorinen: Linear approximation property, Minkowski dimension, and quasiconformal spheres.—J. London Math. Soc. (2) 42 (1990), 249–266

    Article  MATH  MathSciNet  Google Scholar 

  • [N] Nolder, C.A.: A characterization of certain measures using quasiconformal mappings.—Proc. Amer. Math. Soc. 109 (1990), 349–356

    Article  MATH  MathSciNet  Google Scholar 

  • [O1] Oleinik, V.L.: Embedding theorems for weighted classes of harmonic and analytic functions.—J. Soviet Math. 9 (1978), 228–243. (A translation of Zap. Nautsh. Sem. LOMI Steklov. 47 (1974))

    Article  Google Scholar 

  • [O2] Oleinik, V.L.: Estimates for then-widths of compact sets of analytic functions inL p with weight function.—Vestnik Leningradskovo Universiteta, Ser. Math. Mech. 7 (1975), 47–51

    MathSciNet  Google Scholar 

  • [O3] Oleinik, V.L.: An embedding theorem for some classes of analytic functions. (Russian).—Problems of math. physics. Leningrad, Vyp. 11, (1986), 164–167

    MathSciNet  Google Scholar 

  • [OP] Oleinik, V.L. and B.S. Pavlov: Embedding theorems for weighted classes of harmonic and analytic functions.—J. Soviet Math. 2 (1974), 135–142 (A translation of Zap. Nautsh. Sem. LOMI Steklov, 22 (1971), 92–102.)

    Article  MathSciNet  Google Scholar 

  • [R1] Reshetnyak, Yu.G.: Space mappings with bounded distortion.—Translations of mathematical monographs. Vol. 73, (1989), AMS, Providence, Rhode Island

    MATH  Google Scholar 

  • [R2] Reshetnyak, Yu.G.: Stability theorems in geometry and analysis (Russian). —Izdat. “Nauka”, Sibirsk. Otdelenie, Novosibirsk, 1982

    MATH  Google Scholar 

  • [S] Stegenga, D.: Multipliers of the Dirichlet spaces.—Ill. J. Math. 24 (1980), 113–139

    MATH  MathSciNet  Google Scholar 

  • [T] Tsuji, M.: Potential theory.—Maruzen Co. Ltd, Tokyo 1959

    MATH  Google Scholar 

  • [V] Väisälä, J.: Lectures onn-dimensional quasiconformal mappings.—Lecture Notes in Math. 229, Springer-Verlag, 1971

  • [VE] Verbitskii, I.E.: Embedding theorems for spaces of analytic functions with mixed norms.—AN Moldarskoi SSR, Institut of Geophysics and Geology, Kishinev, Preprint 1987, 1–41. (Russian)

  • [VU] Vuorinen, M.: Conformal geometry and quasiregular mappings.—Lecture Notes in Math. Vol. 1319, Springer-Verlag, 1988

Download references

Author information

Authors and Affiliations

  1. Department of Physics, Leningrad State University, 198904, Leningrad, USSR

    V. L. Oleinik & M. Vuorinen

  2. Department of Mathematics, University of Helsinki, 00100, Helsinki, FINLAND

    V. L. Oleinik & M. Vuorinen

Authors
  1. V. L. Oleinik
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. Vuorinen
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

This article was processed by the author using the Springer-Verlag TEX mamath marco package 1990

Rights and permissions

Reprints and permissions

About this article

Cite this article

Oleinik, V.L., Vuorinen, M. Embedding theorems for Bergman spaces in quasiconformal balls. Manuscripta Math 72, 181–203 (1991). https://doi.org/10.1007/BF02568274

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02568274

Keywords

Search

Navigation