Laplace transforms in the weight spaces LP and their applications

For a fixed 0 : |0| < 7r /2, we introduce the function G#(r) = G(re*e), r > 0. We will prove the following theorem.

I f g(t) G Lpa , then G${r) G and

\\Ge\kp < C(p, q, a )(cos0)(1+“ -P)/H|<,||p,a> |0 | < t t /2 .