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On higher order Bessel potentials

Authors:	Email author" target="_blank">A S?Abdel-Rady Email author Email author" target="_blank">H?Begehr Email author

Institution:	(1) Math. Department, Faculty of Science, South Valley University, Qena, Egypt;(2) I. Math. Inst., FU Berlin, Arnimallee 3, 14195 Berlin, Germany

Abstract:	The solutions of the equation $-(\Delta - I)^{k}u_{k} = f, k \geq 1$ in $\mathbb{R}^n$ , where $f \in L^{2} (\mathbb{R}^n)$ are investigated, Bessel potentials of higher order are defined, and recurrence relations between these solutions and these Bessel potentials are obtained. It is also proved that these solutions and the solutions of $-\Delta^{k}v_{k} + v_{k} = \varrho$ , under certain conditions, are identical. Received: 6 November 2002

Keywords:	31B15 31B30 35J30
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