A Note on Maximal Averages in the Plane
  Using variants of the TT* method we give a self-contained proof of the result of Alfonseca, Soria and Vargas on maximal operators on arbitrary directions in $\rr^2$. We also give a sharp $L^2$ estimate for a maximal function extending a Theorem of Cordoba. 
Jose A. Barrionuevo, Lucas Oliveira