In this paper, we consider Hardy space decomposition of L-p(partial derivative D), 0 < p <= 1, where D stands for the open unit disc, and partial derivative D is its boundary. Hardy spaces decompositions for L-p(partial derivative D) and L-p(R) for 1 <= p <= infinity are, as classical results, available in the literature. For 1 <= p <= infinity, the basic tools are the Plemelj formula and the boundedness of the Hilbert transformation. For 0 < p <= 1, neither on the real line, nor on the unit circle, a Plemelj formula, or Hilbert transformation are available. In a recent paper, Deng and Qian obtain Hardy spaces decomposition for L-p(R), 0 < p < 1, on the real line by means of rational approximation. In the present paper using rational functions, we achieve the same goal for L-p(partial derivative D) for the range 0 < p <= 1. The work on the unit circle exposes the particular features of the kind of decomposition in the compact situation adaptable to higher dimensions.

Hardy space; unit disc; decomposition theorem; rational approximation; analytic signal

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