Abstract
In this paper, square-integrable Octonion-valued function spaces on R3 and R7 are decomposed into the direct sum of Octonion Hardy and conjugate Hardy spaces, and square-integrable Octonion function spaces on the upper half spaces R + 4 and R + 8 are decomposed into infinity direct sum of subspaces in which the first components are just the Octonion Bergman spaces. The Octonion Hardy Spaces on R3 and R7 are characterized.
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