A NEW APPROACH TO THE ANALYTICITY OF SOME CLASSES OF ONE-PARAMETER SEMIGROUPS IN WEIGHTED-L-P SPACES

We prove that the operator Au := alpha u '', with alpha epsilon C[0, 1 ] and alpha(x) > 0 in (0,1), generates an analytic C-o-semigroup on L- P((0, 1), 1/alpha) := {u epsilon L-P(0, 1)/ /u/(P) /alpha epsilon L-1( 0, 1)}, 1 < p < infinity, provided that some additional assumptions de pending on the domain of A are required for alpha. The main tools used here are J. Neuberger's sufficient condition for analyticity and the Stein Interpolation Theorem. (C) 1998 Academic Press.