We establish a weighted Hardy space theory associated with flag
structures. This theory differs from those in the classical one-parameter
and the product settings, and includes weighted Hardy spaces
, weighted Carleson
measure spaces
(the
dual spaces of
),
and the boundedness of singular integrals with flag kernels on these spaces. We also derive
a Calderón–Zygmund decomposition and provide interpolation of operators acting
on
.
Examples and counterexamples are constructed to clarify the
relations between classes of one-parameter, product and flag
weights. The main tool for our approach is the weighted Littlewood–Paley–Stein
theory associated with the flag structure.
Keywords
Calderón–Zygmund decomposition, duality, interpolation,
singular integrals with flag kernels, weighted flag
Carleson measure spaces, weighted flag Hardy spaces