臺灣博碩士論文加值系統

In this thesis, we are concerned about a factorization theorem in a certain function space. This theorem was discovered first in the unit disc in C in the first part of the 20th century. In 1976, Coifman, Rochberg and Weiss extended it to the unit ball in C^n. In 1992, Krantz and Li proved that it holds on smoothly bounded strongly pseudoconvex domains. And Lin proved that it is true for the bi-upper half plane in 1996, and Wu proved it for the triple-upper half plane for p=1 in 2000. Does it hold for the triple-upper half plane and the triple-disc for 0<p<=1?
A factorization theorem is proved in the Hardy spaces H^p of triple-upper half plane, 0<p<=1, in which case it is based on some fundamental work of Chang-Fefferman and Fefferman-Stein, on atomic decompositions and duality of the spaces BMO and H^1.
From the result of the factorization theorem in the Hardy spaces H^p of triple-upper half plane, 0<p<=1 and the Cayley Transform, we prove the factorization theorem in the Hardy spaces H^p of triple-disc, 0<p<=1.
This thesis is used to prepare for generalization of the factorization theorem.

In this thesis, we are concerned about a factorization theorem in a certain function space. This theorem was discovered first in the unit disc in C in the first part of the 20th century. In 1976, Coifman, Rochberg and Weiss extended it to the unit ball in C^n. In 1992, Krantz and Li proved that it holds on smoothly bounded strongly pseudoconvex domains. And Lin proved that it is true for the bi-upper half plane in 1996, and Wu proved it for the triple-upper half plane for p=1 in 2000. Does it hold for the triple-upper half plane and the triple-disc for 0<p<=1?
A factorization theorem is proved in the Hardy spaces H^p of triple-upper half plane, 0<p<=1, in which case it is based on some fundamental work of Chang-Fefferman and Fefferman-Stein, on atomic decompositions and duality of the spaces BMO and H^1.
From the result of the factorization theorem in the Hardy spaces H^p of triple-upper half plane, 0<p<=1 and the Cayley Transform, we prove the factorization theorem in the Hardy spaces H^p of triple-disc, 0<p<=1.
This thesis is used to prepare for generalization of the factorization theorem.

1.Introducion
2.Factorization Theorem in Hardy Space of Triple-upper Half Plane(0<p<=1)
3.Factorization in Hardy Space of the Triple-disc(0<p<=1)
3.1 The Cayley Transform
3.2 Factorization Theorem
Reference

E. M. Stein and G. Weiss, "On the theory of H^p spaces", Acta Math. 103(1960), 25-62
Ing-Jer Lin, "Factorization theorem for Hardy spaces of bidisc", proceeding of the Amer. Math. Soc. 124, No 2, February(1996), 549-560
Ing-Jer Lin and Bernard Russo, "An application of Factorization in the Hardy spaces of the polydisc", Lecture notes in pure and applied mathematics. 175(1996), 331-349.
John B. Conway, "A Course in Functional Analysis", Springer-Verlag
John B. Garnett, "Bounded Analysis Functions", Academic Press, 1981.
R. Coifman, R. Rochberg and G. Weiss, "Factorization theorems for Hardy spaces in several variables", Ann. of Math, 103(1976), 611-635.
Sun-Yung A. Chang and Robert Fefferman, "A continous version of duality of H^1 with BMO on the bidisc", Ann of Math. 110(1979), 613-620.
Sun-Yung A. Chang and Robert Fefferman, "The Calderon-Zymund Decomposition on Product Domains", American Journal of Math. 112(1980), 179-201
Walter Rudin, "Funcion Theory in Polydisc", W. A. Benjamin, Inc.
Walter Rudin, "Function Theory in the Unit Ball of C^n", Springer-Verlag
Walter Rudin, "Real and Complex Analysis", Mei Ya Publications, Inc. 1974