$L\log \log L$ versions of Stein's and Zygmund's theorems for the Hardy space $H^{\log }({\mathbb{R}}^d)$

Odysseas Bakas, Salvador Rodríguez-López, Alan Sola

We obtain versions of some classical results of Zygmund and Stein for functions belonging to the Hardy space $H^{\log }({\mathbb{R}}^d)$ introduced by Bonami, Grellier, and Ky. We pr…