FLAG HARDY SPACES AND MARCINKIEWICZ MULTIPLIERS ON THE HEISENBERG GROUP

By Yongsheng Han, G. Lu, Eric T. Sawyer. 2012

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product on C n R developed by A. Chang and R. Fefferman. We show that flag singular integral operators, which include the aforementioned Marcinkiewicz multipliers, are bounded on H p flag , as well as from H p flag to L p , for 0< p 1. We also characterize the dual spaces of H 1 flag and H p flag , and establish a Calderon‐Zygmund decomposition that yields standard interpolation theorems for the flag Hardy spaces H p flag. In particular, this recovers some L p results of Muller, Ricci, and Stein (but not their sharp versions) by interpolating between those for H p flag and L 2 .

Subfields: Applied Mathematics

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