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Factorization theorems for Hardy spaces of the bidisc, $0<p\le1$

Author(s): Ing-Jer Lin
Journal: Proc. Amer. Math. Soc. 124 (1996), 549-560.
MSC (1991): Primary 32A35, 42B30, 32A10, 32H10, 46E35; Secondary 30D55, 26A16
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Abstract: A factorization theorem is proved in the Hardy spaces $H^p$ of the bi-upper half plane, $0<p\le1$. The proof is based on some fundamental work of Chang-Fefferman on atomic decompositions of $H^p$.

References:

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S.-Y. A. Chang and R. Fefferman A continuous version of duality of $H^1$ with BMO on the bidisc, Ann. of Math. (2) 112 (1980), 179--201. MR 82a:32009

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------ The Calderon-Zymund decomposition on product domains, Amer. J. Math. 104 (1982), 455--468. MR 84a:42028

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R. Coifman A real variable characterization of $H^p$, Studia Math. 51 (1974), 269--274. MR 50:10784

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R. Coifman, R. Rochberg, and G. Weiss Factorization theorem for Hardy spaces in several variables, Ann. of Math. (2) 103 (1976), 611--635. MR 54:843

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S. G. Krantz Function theory of several complex variables, Wadsworth and Brooks/Cole, Belmont, CA, 1992. MR 93c:32001

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S. G. Krantz and Song-Ying Li On the decompositions for Hardy spaces in domains in $C^n$ and applications, preprint, 1992.

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R. Latter A characterization of $H(\mathbf R^n)^p$ in terms of atoms, Studia Math. 62 (1978), 93--101. MR 58:2198

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E. M. Stein Singular integrals and differentiability properties of functions, Princeton Univ. Press, Princeton, NJ, 1970. MR 44:7280

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Additional Information:

Ing-Jer Lin
Affiliation: Department of Mathematics, National Kaohsiung Normal University, Taiwan 80264
Email: t1265@nknucc.nknu.edu.tw

DOI: 10.1090/S0002-9939-96-03193-0
PII: S 0002-9939(96)03193-0
Received by editor(s): September 7, 1994
Communicated by: Palle E. T. Jorgensen
Copyright of article: Copyright 1996, American Mathematical Society

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