A remark on maximal operators along directions in ${\Bbb R}^2$
A remark on maximal operators along directions in ${\Bbb R}^2$
In this paper we give a simple proof of a long-standing conjecture, recently proved by N. Katz, on the weak-type norm of a maximal operator associated with an arbitrary collection of directions in the plane.The proof relies upon a geometric argument and on induction with respect to the number of …