We discuss the result  of Müller, Ricci, Wright about the nature of the Lebesgue points of the Fourier transform of an $L^p$ function and in particular if Fourier restriction to convex curves holds in the sense of Lebesgue differentiation. To do so we must study a maximal-type restriction operator.
We will show the boundedness of this operator in a slightly more general setting than initially considered in .
 Müller, D., Ricci, F., & Wright, J. (2016). A maximal restriction theorem and Lebesgue points of functions in F (L^ p). arXiv preprint