ABSTRACT
Every term in the right-hand side of this estimate tends to zero as (t,S) -. (to,so). In fact, for the first two terms this follows from (13.30) and the boundedness of the function X, for the third term from the continuity of the function t 1-+ Lnx(t, 80} I and for the fourth term from the continuity of the function x and formula (13.21) for the norm of P. We conclude that Lx E C(D), hence L E .c,(C}.
