Hardy space of exact forms on

Authors:
Zengjian Lou and Alan McIntosh

Journal:
Trans. Amer. Math. Soc. **357** (2005), 1469-1496

MSC (2000):
Primary 42B30; Secondary 35J45, 58A10

DOI:
https://doi.org/10.1090/S0002-9947-04-03535-4

Published electronically:
September 2, 2004

MathSciNet review:
2115373

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We show that the Hardy space of divergence-free vector fields on has a divergence-free atomic decomposition, and thus we characterize its dual as a variant of . Using the duality result we prove a ``div-curl" type theorem: for in , is equivalent to a -type norm of , where the supremum is taken over all with This theorem is used to obtain some coercivity results for quadratic forms which arise in the linearization of polyconvex variational integrals studied in nonlinear elasticity. In addition, we introduce Hardy spaces of exact forms on , study their atomic decompositions and dual spaces, and establish ``div-curl" type theorems on .

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Additional Information

**Zengjian Lou**

Affiliation:
Institute of Mathematics, Shantou University, Shantou Guangdong 515063, People’s Republic of China

Email:
zjlou@stu.edu.cn

**Alan McIntosh**

Affiliation:
Center for Mathematics and its Applications, Mathematical Sciences Institute, the Australian National University, Canberra, Australian Capital Territory 0200, Australia

Email:
alan@maths.anu.edu.au

DOI:
https://doi.org/10.1090/S0002-9947-04-03535-4

Keywords:
Divergence-free Hardy space,
Hardy space of exact forms,
atomic decomposition,
$BMO$,
div-curl,
coercivity

Received by editor(s):
May 16, 2003

Received by editor(s) in revised form:
October 19, 2003

Published electronically:
September 2, 2004

Additional Notes:
The authors are supported by the Australian Government through the Australian Research Council. This paper was written when both authors were at the Center for Mathematics and its Applications of the Mathematical Sciences Institute at the Australian National University.

Article copyright:
© Copyright 2004
American Mathematical Society