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A div-curl decomposition for the local Hardy space

Author(s): Der-Chen Chang; Galia Dafni; Hong Yue
Journal: Proc. Amer. Math. Soc. 137 (2009), 3369-3377.
MSC (2000): Primary 42B30; Secondary 35B65, 35F05, 46E35
Posted: May 21, 2009
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Abstract: A decomposition theorem for the local Hardy space of Goldberg, in terms of nonhomogeneous div-curl quantities, is proved via a dual result for the space bmo.

References:

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Bonami, A., Iwaniec, T., Jones, P., Zinsmeister, M.: On the product of functions in BMO and $ H\sp 1$, Ann. Inst. Fourier (Grenoble) 57 (2007), pp. 1405-1439. MR 2364134 (2009d:42054)

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Coifman, R., Lions, P.-L., Meyer,Y., Semmes, S.: Compensated compactness and Hardy spaces, J. Math. Pures Appl. 72 (1993), pp. 247-286. MR 1225511 (95d:46033)

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Dafni, G.: Nonhomogeneous div-curl lemmas and local Hardy spaces, Adv. Differential Equations 10 (2005), pp. 505-526. MR 2134048 (2006a:42030)

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Fefferman, C., Stein, E. M.: $ H^p$ spaces of several variables, Acta Math. 129 (1972), pp. 137-193. MR 0447953 (56:6263)

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Girault, V., Raviart, P.-A.: Finite Element Methods for Navier-Stokes Equations: Theory and Algorithms, Springer-Verlag, Berlin, 1980. MR 851383 (88b:65129)

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Goldberg, D.: A local version of real Hardy spaces, Duke Math. J. 46 (1979), pp. 27-42. MR 523600 (80h:46052)

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Additional Information:

Der-Chen Chang
Affiliation: Department of Mathematics, Georgetown University, Washington, DC 20057
Email: chang@georgetown.edu

Galia Dafni
Affiliation: Department of Mathematics and Statistics, Concordia University, Montreal, Quebec, H3G 1M8, Canada
Email: gdafni@mathstat.concordia.ca

Hong Yue
Affiliation: Department of Mathematics and Informatics, Trine University, Angola, Indiana 46703
Email: yueh@trine.edu

DOI: 10.1090/S0002-9939-09-09970-5
PII: S 0002-9939(09)09970-5
Received by editor(s): January 21, 2009
Posted: May 21, 2009
Additional Notes: The first author was partially supported by a Hong Kong RGC competitive earmarked research grant \#600607 and a competitive research grant at Georgetown University.
The second author was partially supported by the Natural Sciences and Engineering Research Council, Canada
The third author was partially supported by the Natural Sciences and Engineering Research Council, Canada, and the Centre de Recherches Mathématiques, Montreal
Communicated by: Mei-Chi Shaw
Copyright of article: Copyright 2009, Der-Chen Chang, Galia Dafni, and Hong Yue

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