The sharp constant in the weak (1,1) inequality for the square function: a new proof
Irina HolmesTexas A&M University, College Station, USA
Paata IvanisviliPrinceton University, USA and University of California, Irvine, USA
Alexander VolbergMichigan State University, East Lansing, USA
In this note we give a new proof of the sharp constant in the weak (1, 1) inequality for the dyadic square function. The proof makes use of two Bellman functions and related to the problem, and relies on certain relationships between and , as well as the boundary values of these functions, which we find explicitly. Moreover, these Bellman functions exhibit an interesting behavior: the boundary solution for yields the optimal obstacle condition for , and vice versa.
Cite this article
Irina Holmes, Paata Ivanisvili, Alexander Volberg, The sharp constant in the weak (1,1) inequality for the square function: a new proof. Rev. Mat. Iberoam. 36 (2020), no. 3, pp. 741–770DOI 10.4171/RMI/1147