An extension of the Córdoba-Fefferman theorem on the equivalence between the boundedness of certain classes of maximal and multiplier operators

The Córdoba-Fefferman theorem involving the equivalence between boundedness properties of certain classes of maximal and multiplier operators is extended utilizing the recent work of Bateman on directional maximal operators as well as the work of Hagelstein and Stokolos on geometric maximal operators associated to homothecy invariant bases of convex sets satisfying Tauberian conditions. To cite this article: P. Hagelstein, A. Stokolos, C. R. Acad. Sci. Paris, Ser. I 346 (2008).