Hardy space

In complex analysis, the Hardy spaces are analogues of the Lp spaces of functional analysis. They are named for G. H. Hardy.

For example for spaces of holomorphic functions on the open unit disc, the Hardy space H² consists of the functions f whose mean square value on the circle of radius r remains finite as r -> 1 from below.

Such spaces have a number of applications in mathematical analysis itself, and also to control theory and scattering theory. A space H² may sit naturally inside an L² space as a 'causal' part, for example represented by infinite sequences indexed by N, where L² consists of bi-infinite sequences indexed by Z.