With these Hardy inequalities, the Hardy inequalities on rearrangement-invariant Hardy space
are established by using the interpolation functor introduced in .
The invariant subspaces of Volterra integral operator on the Hilbert Hardy space
is studied by Donoghue , and a complete characterization of such subspaces in a Banach spaces of analytic functions in the open unit disc, containing the Hardy, Bergman and Dirichlet spaces is obtained in 2008 by Aleman and Korenblum in .
It is proved that the maximal operator of the [theta]-means defined in a cone is bounded from the local Hardy space
They are everywhere defined in some special cases on the classical Hardy Space
For p [member of][1, [infinity]) the Hardy space
n] leads to a better understanding of the deviation from the classical Hardy space
of the disk setting.
For instance the classical theorem of Beurling  on the structure of analytically invariant subspaces of the Hardy space
on the torus has been influential in many areas of modern mathematics, ranging from the dilation theory of a contraction, to interpolation problems in function theory or to the probabilistic analysis of time series.
phi]] on the Hardy space
, when [phi] is rational self-map of the unit disk U.
infinity]], this space is the dual space of the weighted Hardy space
Three classical examples of p-Frechet spaces, non-locally convex, are the Hardy space
WIELONSKY, On a rational approximation problem in the real Hardy space
In , Shapiro and Taylor considered the Hilbert-Schmidtness of composition operators on the Hilbert Hardy space
and moreover characterized results related to the Dirichlet space.