In this paper, we develop via real variable methods various characterisations of the Hardy spaces in the multi-parameter flag setting. These characterisations include those via, the non-tangential and radial maximal function, the Littlewood-Paley square function and area integral, Riesz transforms and the atomic decom-position in the multi-parameter flag setting. The novel ingredients in this paper include (1) establishing appropriate discrete Calderon reproducing formulae in the flag setting and a version of the Plancherel-Polya inequalities for flag quadratic forms; (2) introducing the maximal function and area function via flag Poisson kernels and flag version of harmonic functions; (3) developing an atomic decom-position via the finite speed propagation and area function in terms of flag heat semigroups. As a consequence of these real variable methods, we obtain the full characterisations of the multi-parameter Hardy space with the flag structure.

About the Author
Yongsheng Han, Auburn University, GA.

Ming-Yi Lee, National Central University, Chung-Li, Taiwan, and National Center for Theoretical Sciences, Taipei, Taiwan.

Ji Li, Macquarie University, Sydney, Australia.

Brett Wick, Washington University, St. Louis, Missouri.


Book Information
ISBN 9781470453459
Author Yongsheng Han
Format Paperback
Page Count 102
Imprint American Mathematical Society
Publisher American Mathematical Society
Weight(grams) 363g