Factorization theorems for Hardy spaces of the bidisc, $0 < p \le 1$
HTML articles powered by AMS MathViewer
- by Ing-Jer Lin PDF
- Proc. Amer. Math. Soc. 124 (1996), 549-560 Request permission
Abstract:
A factorization theorem is proved in the Hardy spaces $H^p$ of the bi-upper half plane, $0<p\le 1$. The proof is based on some fundamental work of Chang-Fefferman on atomic decompositions of $H^p$.References
- Sun-Yung A. Chang and Robert Fefferman, A continuous version of duality of $H^{1}$ with BMO on the bidisc, Ann. of Math. (2) 112 (1980), no. 1, 179–201. MR 584078, DOI 10.2307/1971324
- Sun-Yung A. Chang and Robert Fefferman, The Calderón-Zygmund decomposition on product domains, Amer. J. Math. 104 (1982), no. 3, 455–468. MR 658542, DOI 10.2307/2374150
- Ronald R. Coifman, A real variable characterization of $H^{p}$, Studia Math. 51 (1974), 269–274. MR 358318, DOI 10.4064/sm-51-3-269-274
- R. R. Coifman, R. Rochberg, and Guido Weiss, Factorization theorems for Hardy spaces in several variables, Ann. of Math. (2) 103 (1976), no. 3, 611–635. MR 412721, DOI 10.2307/1970954
- Steven G. Krantz, Function theory of several complex variables, 2nd ed., The Wadsworth & Brooks/Cole Mathematics Series, Wadsworth & Brooks/Cole Advanced Books & Software, Pacific Grove, CA, 1992. MR 1162310
- S. G. Krantz and Song-Ying Li On the decompositions for Hardy spaces in domains in $C^n$ and applications, preprint, 1992.
- Robert H. Latter, A characterization of $H^{p}(\textbf {R}^{n})$ in terms of atoms, Studia Math. 62 (1978), no. 1, 93–101. MR 482111, DOI 10.4064/sm-62-1-93-101
- Elias M. Stein, Singular integrals and differentiability properties of functions, Princeton Mathematical Series, No. 30, Princeton University Press, Princeton, N.J., 1970. MR 0290095
Additional Information
- Ing-Jer Lin
- Email: t1265@nknucc.nknu.edu.tw
- Received by editor(s): September 7, 1994
- Communicated by: Palle E. T. Jorgensen
- © Copyright 1996 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 124 (1996), 549-560
- MSC (1991): Primary 32A35, 42B30, 32A10, 32H10, 46E35; Secondary 30D55, 26A16
- DOI: https://doi.org/10.1090/S0002-9939-96-03193-0
- MathSciNet review: 1307547