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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 H p F,w, weighted Carleson measure spaces CMOp F,w (the dual spaces of H p F,w), 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 H p F,w. Examples and counterexamples are constructed to clarify the relations between classes of one-parameter, product and flag Ap weights. The main tool for our approach is the weighted Littlewood-Paley- Stein theory associated with the flag structure.
- Calderón-Zygmund decomposition
- Singular integrals with flag kernels
- Weighted flag Carleson measure spaces
- Weighted flag Hardy spaces
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