Pacific Journal of Mathematics

On the uniform approximation problem for the square of the Cauchy-Riemann operator.

Joan Verdera

Article information

Pacific J. Math., Volume 159, Number 2 (1993), 379-396.

First available in Project Euclid: 8 December 2004

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 30E10: Approximation in the complex domain
Secondary: 35N99: None of the above, but in this section


Verdera, Joan. On the uniform approximation problem for the square of the Cauchy-Riemann operator. Pacific J. Math. 159 (1993), no. 2, 379--396.

Export citation


  • [1] J.J.Carmona,MergelyarCs approximation theoremforrational modules J. Ap- prox. Theory, 44(1985), 113-125.
  • [2] J.Deny, Systemes totaux defunctions harmoniques,Ann. Inst. Fourier, 1(1949), 103-113.
  • [3] T.W.Gamelin, UniformAlgebras,Prentice-Hall, Englewood Cliffs, N.J., 1969.
  • [4] J.Garnett, Analytic Capacity andMeasure, Lecture Notes inMath., vol 297, Springer-Verlag, Berlin and New York, 1972.
  • [5] L.I.Hedberg, Two approximation problems infunctions spaces,Ark.Mat.,16 (1978), 51-81.
  • [6] M.V.Keldysh, Onthesolubility andstability of the Dirichlet problem, Amer. Math. Soc. TransL, (2)51(1966), 1-73.
  • [7] J.Mateu and J. Verdera, BMO harmonic approximation in theplane andspectral synthesis for Hardy-Sobolev spaces, Revista Matem. Iberoamericana, 4 (1988), 291-318.
  • [8] M.Melnikov andJ. Orobitg, A counterexample to a Vitali type theoremfor planar sets andonedimensional Hausdorff content, toappear inProc. Amer. Math. Soc.
  • [9] E. M.Stein, Singular integrals anddifferentiability properties of functions, Princeton Univ. Press, Princeton, N.J., 1970.
  • [10] T. Trent and J. L. Wang, Uniform approximation by rational modules on no- where dense sets, Proc. Amer. Math. So,81 (1981),62-64.
  • [11] A. G. Vitushkin, Analytic capacity of sets in problems of approximation theory, Russian Math. Surveys, 22 (1967), 139-200.
  • [12] J. L. Wang, A localization operator for rational modules, Rocky Mountain J. Math., 19 (1989),999-1002.