#### Function spaces and composition properties of holomorphic functions on the unit ball of Cn = 단위구상의 해석함수들의 함수공간과 합성연산

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The purpose of this thesis is to study the functional analytic and function theoretic properties of certain class of function spaces which consist of holomorphic functions on $B_n$ and to deal with related problems. In Chapter 2 we compute the dual spaces of a Hardy space $H^p(B_n)$ ($0 < p <1$) and a weighted Bergman space $A^p(B_n)$ ($0 < P <1$, $\alpha > -1$). The crucial points in our analysis of these spaces are explicit determinations of their Mackey topologies using an "atomic decomposition" of the same sort discussed by Shapiro in [18]. The corresponding problems for the case n = 1 are settled by Duren, Romberg and Shields[10] Shapiro[18] and Ahern and Jevticc[2]. In Chapter 3 we investigate the composition preoperty of a nonhomogeneous bounded holomorphic function. The homogeneous polynomials $n^{n/2}z_1z_2\cdots{z_n},z_1^2+z_2^2+\cdots+z_n^2$ and $b_\alpha{z_1^\alpha1}z_2^\alpha2\cdots{z_p^\alpha{p}}$ ($b_\alpha$ properly chosen) have been known to pull a Bloch function in the unit disc U back to a holomorphic function in the unit ball $B_n$ of bounded mean oscillation. We show that the nonhomogeneous holomorphic function $\pi$n,m(z) $\frac{z_m^2+1+\cdots+z_n^2}{1-(z_1^2+\cdots+z_n^2}$ pulls the Bloch space B(U) back to \$\cap_{0
Kim, Hong-Ohresearcher김홍오researcher
Description
한국과학기술원 : 응용수학과,
Publisher
한국과학기술원
Issue Date
1989
Identifier
61285/325007 / 000845327
Language
eng
Description

학위논문(박사) - 한국과학기술원 : 응용수학과, 1989.8, [ [iv], 81 p. ; ]

URI
http://hdl.handle.net/10203/41757