Abstract We show that the Hilbert transform does not map 𝐿¹(𝑀Φ𝑤) to 𝐿¹,∞(𝑤) for every Young function Φ growing more slowly than 𝑡 log log(𝖾𝖾+𝑡). Our proof is based on a construction of M.C.

When Hannah Cairo started showing up at Berkeley Math Circle meetings as a teenager, nobody was betting she would topple a four-decade-old problem in harmonic analysis before she finished high school.

We find an infinitely-connected graph in which every spanning tree has a 2-way infinite path. This disproves Halin's well-known "end-faithful spanning tree" conjecture and also disproves a recent ...