A Note on Maximal Averages in the Plane

Abstract

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.

References in corpus (2)

• An Estimate of the Maximal Operators Associated with Generalized Lacunary Sets
• Kakeya Sets and Directional Maximal Operators in the Plane