The weak-type Carleson theorem via wave packet estimates

Francesco Di Plinio, Anastasios Fragkos

We prove that the weak-$L^p$ norms, and in fact the sparse $(p,1)$-norms, of the Carleson maximal partial Fourier sum operator are $\lesssim (p-1{)}^{-1}$ as $p\to 1^{+}$. This is an…