On Some Degenerate Differential Operators on Weighted Function Spaces

We deal with the degenerate differential operator Au x.[a x.u0 x. xG0. 0 2 x w. . . defined for every u g W2 l C 0, q` satisfying limxª0q a x u0 x s limxªq` a x.r 1qx2 ..u0 x.s0. Here W20 denotes the Banach space of all continuous functions f : w0,q`wªR such that f x.r 1qx2 . vanishes at infinity, endowed with the weighted norm 5 f 5 2[supxG0 < f x.