Journal of Mathematical Sciences

, Volume 92, Issue 6, pp 4404–4411 | Cite as

The green functions for weighted biharmonic operators of the form Δω−1Δ in the unit diskin the unit disk

  • S.M. Shimorin


In the unit disk of the complex plane, the Green functions for weighted biharmonic operators of the form Δω−1Δ are studied. The Green function is nonnegative everywhere if the weight function w is radial, logarithmically subharmonic, and area integrable. In the case of weighted Bergman classes, this fact allows us to establish the existence of a factorization of functions similar to the interior-exterior factorization in Hardy classes. Bibliography: 6 titles.


Weight Function Harmonic Function Green Function Unit Disk Bergman Space 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    H. Hedenmalm, “A factorization theorem for square area-integrable analytic functions,”J. Reine Angew. Math.,422, 45–68 (1991).MATHMathSciNetGoogle Scholar
  2. 2.
    P. Duren, D. Khavinson, H. S. Shapiro, and C. Sundberg, “Contractive zero-divisors in Bergman spaces,”Pacific J. Math.,157, No. 1, 37–56 (1993).MATHMathSciNetGoogle Scholar
  3. 3.
    H. Hedenmalm, “A computation of Green functions for the weighted biharmonic operators Δ|z|−2αΔ, with α> −1,”Duke Math. J.,75, 51–78 (1994).MATHMathSciNetCrossRefGoogle Scholar
  4. 4.
    S. M. Shimorin, “Green's functions for weighted biharmonic operators Δ(1−)|z|2)−αΔ and factorization of analytic functions,”Zap. Nauchn. Sem. POMI,222, 203–221 (1995).MATHGoogle Scholar
  5. 5.
    H. Hedenmalm, “Boundary value problems for weighted biharmonic operators,”Algebra Analiz, to appear.Google Scholar
  6. 6.
    S. M. Shimorin, “Single-point extremal functions in weighted Bergman spaces,”J. Math. Sci.,80, No. 6, 2349–2356 (1996).MathSciNetCrossRefGoogle Scholar

Copyright information

© Plenum Publishing Corporation 1998

Authors and Affiliations

  • S.M. Shimorin

There are no affiliations available

Personalised recommendations