The Franklin system is an unconditional basis in \(H_ 1\) (Q790386)

Recently, \textit{L. Carleson} [Bull. Sci. Math., II. Ser. 104, 405-416 (1980; Zbl 0495.46020)] exhibited an explicit sequence of BMO functions whose biorthogonal functionals form an unconditional basis for \(H^ 1\). The present work modifies this construction so as to obtain an orthonormal set of piecewise continuous functions on the interval [0,1] (called a ''Franklin system'') which forms an unconditional \(H^ 1\) basis. Among the consequences of this, one obtains an unconditional basis for the space of Hankel operators.