The behaviour on radial functions of maximal operators along arbitrary directions and the Kakeya maximal operator (Q749797)

The behaviour of the Kakeya and universal maximal operators on radial functions is considered. If \(M_ N\) is the maximal function associated to N arbitrary directions in \({\mathbb{R}}^ n\), it is asserted that the strong (resp. weak) type \(L^ n\)-norm of \(M_ N\), when acting on radial functions, is O(log N) (resp. O((log N)\({}^{(n-1)/n}))\). The erratum (cited below) corrects an error in the main paper. Theorems 1 and 2 of the main paper remain valid but the application to Cantor sets is invalidated by the error.