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Abstract
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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.
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Keywords
Calderón–Zygmund decomposition, duality, interpolation,
singular integrals with flag kernels, weighted flag
Carleson measure spaces, weighted flag Hardy spaces
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Mathematical Subject Classification 2010
Primary: 42B20
Secondary: 42B30
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Milestones
Received: 13 December 2017
Revised: 22 January 2019
Accepted: 27 February 2019
Published: 27 November 2019
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