We give a new characterization of Hardy martingale cotype property of complex quasi-Banach space by using the existence of a kind of plurisubharmonic functions. We also characterize the best constants of Hardy martingale inequalities with values in the complex quasi-Banach space.

Keywords:

Hardy martingale, Hardy martingale cotype, plurisubharmonic function Hardy martingale, Hardy martingale cotype, plurisubharmonic function

MSC Classifications:

46B20, 52A07, 60G44 show english descriptions Geometry and structure of normed linear spaces
Convex sets in topological vector spaces [See also 46A55]
Martingales with continuous parameter 46B20 - Geometry and structure of normed linear spaces
52A07 - Convex sets in topological vector spaces [See also 46A55]
60G44 - Martingales with continuous parameter

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