L ^p improving estimates for some classes of Radon transforms

In this paper, we give L ^p - L ^q estimates and the L ^F regularizing estimate of Radon transforms associated to real analytic functions, and we also give estimates of the decay rate of the L ^p operator norm of corresponding oscillatory integral operators. For L ^p - L ^q estimates and estimates of the decay rate of the L ^p operator norm we obtain sharp results except for extreme points; however, for L ^p regularity we allow some restrictions on the phase function.