The $L(\log L{)}^{\epsilon }$ endpoint estimate for maximal singular integral operators

Tuomas Hytönen, Carlos Pérez

We prove in this paper the following estimate for the maximal operator $T^{\ast }$ associated to the singular integral operator $T$: $ \|T^*f\|_{L^{1,\infty}(w)} \lesssim \frac{1}ε \int_…