Lp Improving Estimates for Some Classes of Radon Transforms

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