1](U) where f and [sigma] are Borel measurable maps from I x E x E x U to E and [Laplace] (H, E) respectively.
1 hold and that l and [PHI] are Borel measurable real valued functions on I x E x E x [M.
More precisely, we assume that f : D x [0, [infinity]) [right arrow] [0, [infinity]) is Borel measurable function satisfying
A Borel measurable function q in D belongs to the Kato class K(D) if
sigma] is Borel measurable
and there exist positive constants [a.
Throughout the paper, let G be a locally compact group with a fixed left Haar measure [lambda] and [omega] be a weight function on G; that is, a positive Borel measurable
function on G.