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http://dx.doi.org/10.4134/JKMS.2006.43.6.1169

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)
Publication Information
Journal of the Korean Mathematical Society / v.43, no.6, 2006 , pp. 1169-1181 More about this Journal
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.
Keywords
Poisson kernel; biharmonic function; biharmonic Green function; convergence in the mean; Fatou's theorem;
Citations & Related Records

Times Cited By Web Of Science : 1  (Related Records In Web of Science)
Times Cited By SCOPUS : 1
연도 인용수 순위
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   DOI