The full range of Sobolev endpoint regularity of Radon transform is given. We prove the failure of endpoint regularity for real analytic phases. The critical endpoint regularity $L^p(\bR^2)\rightarrow L^p_s(\bR^2)$ is true if only and only if $p=2$. This generalizes a result of M. Christ. In particular, it implies that the Radon transform is not bounded from $L^p$ into $L^p_{1/n}$, where phase functions are $S(x,y)=a_1x^{n-1}y+a_2x^{n-2}y^2+\cdots+a_{n-1}xy^{n-1}$ with $n\geq 3$, the coefficients are real numbers satisfying $a_1a_{n-1}\neq0$, and $p$ is equal to $\frac{n}{n-1}$ or $n$. This answers a problem of Phong and Stein in \cite{PS1994}.

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