The Hardy spaces H2(B) and H2(H+), where B and H+ denote, respectively, the open unit ball of the quaternions and the half space of quaternions with positive real part, as well as Blaschke products, have been intensively studied in a series of papers where they are used as a tool to prove other results in Schur analysis. This paper gives an overview on the topic, collecting the various results available.
D. Alpay, F. Colombo and I. Sabadini. Quaternionic Hardy spaces in the open unit ball and half space and Blaschke products. J. Phys.: Conf. Ser. 597 012009, (2015).
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This article was originally published in Journal of Physics: Conference Series , volume 597, in 2015. DOI: 10.1088/1742-6596/597/1/012009