The Sharp Constant in the Weak (1,1) Inequality for the Square Function: A New Proof

Irina Holmes, Paata Ivanisvili, Alexander Volberg

In this note we give a new proof of the sharp constant $C=e^{-1/2}+{\int }_0^1{e}^{-x^2/2}dx$ in the weak (1, 1) inequality for the dyadic square function. The proof makes use of…