A representation theory for bicomplex-valued functions in Hardy classes that generalizes the classical complex holomorphic Hardy spaces on the unit disc. Using the idempotent decomposition into complex components together with the nonhomogeneous Cauchy-Riemann equation and the Cauchy-Pompeiu formula, these functions are shown to have boundary values in the sense of distributions that admit an atomic decomposition, and the Hilbert transform is shown to be continuous on the resulting class of distributional boundary values.
This paper develops representation formulas for bicomplex-valued functions in Hardy classes, which generalize the classical complex holomorphic Hardy spaces on the unit disc. Exploiting the idempoten…