THE RADON-TRANSFORM IS AN ISOMORPHISM BETWEEN L(2)(B-A) AND H-E(Z(A))

It is proved that the radon transform R is an isomorphism between X := L(2)(B-a) and Y := H-e(Z(a)), where B-a is the-ball of radius a cente red at the origin in R(n), n greater than or equal to 2, and Z(a) := S -n-1 x [-a,a], S-n-1 is the unit sphere in R(n), and H-e(Z(a)) is the space of even functions g(alpha,p) which vanish at p = +/-a, satisfy t he moment conditions,and have finite norm (integral(Sn-1) integral(-in finity)(infinity) \Fg\ (1 + lambda(2))((n-1)/2) d lambda d alpha)(1/2) := \g\ < infinity.