Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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A NEW BIHARMONIC KERNEL FOR THE UPPER HALF PLANE

  • Abkar, Ali (Faculty of Mathematics Statistics and Computer Science University College of Science The University of Tehran)
  • Published : 2006.11.01
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Abstract

We introduce a new biharmonic kernel for the upper half plane, and then study the properties of its relevant potentials, such as the convergence in the mean and the boundary behavior. Among other things, we shall see that Fatou's theorem is valid for these potentials, so that the biharmonic Poisson kernel resembles the usual Poisson kernel for the upper half plane.

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References

  1. A. Abkar and H. Hedenmalm, A Riesz representation formula for super-bi- harmonic functions, Ann. Acad. Sci. Fenn. Math. 26 (2001), no. 2, 305-324
  2. P. R. Garabedian, Partial Differential Equations, John Wiley & Sons, Inc., New York-London-Sydney, 1964
  3. J. B. Garnett, Bounded Analytic Functions, Academic Press, New York, 1981
  4. H. Hedenmalm, A computation of Green functions for the weighted biharmonic operators ${\Delta}|z|^{-2{\alpha}}{\Delta}$ with ${\alpha}>-1$ Duke Math. J. 75 (1994), no. 1, 51-78 https://doi.org/10.1215/S0012-7094-94-07502-9

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