Function spaces and composition properties of holomorphic functions on the unit ball of Cn단위구상의 해석함수들의 함수공간과 합성연산

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dc.contributor.advisorKim, Hong-Oh-
dc.contributor.authorChoa, Jun-Soo-
dc.description학위논문(박사) - 한국과학기술원 : 응용수학과, 1989.8, [ [iv], 81 p. ; ]-
dc.description.abstractThe 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 $\cap_{0<p<\infty}H^P(B_n)$. Chapter 4 is concerned with Cauchy integral equalities(CIE). We find a concrete characterization of $\pi\in{P_{2,k}}$(homogeneous polynomials in $C^n$ of degree k) satisfying CIE in some special cases. If $\pi\in{P_{2,k}}$ with k $\leq$ 3 or $\pi\in{P_{2,k}}$ with real coefficients satisfies CIE, then it is shown that $\pi$ can be transformed into a monomial by a unitary change of variables. When $\pi\in{P_{3,2}}$ a slight different characterization is obtained. In this case it is shown that $\pi$ can be transformed, by a unitary change of variables, into a monomial or a sum-of-squares, $az_1^2\,+\,bz_2^2\,+\,cz_3^2$, where $\mid{a}\mid$ = $\mid{b}\mid$ = $\mid{c}\mid$ = 1. In Chapter 5, we deal with a cert...eng
dc.titleFunction spaces and composition properties of holomorphic functions on the unit ball of Cn-
dc.title.alternative단위구상의 해석함수들의 함수공간과 합성연산-
dc.description.department한국과학기술원 : 응용수학과, -
dc.contributor.localauthorKim, Hong-Oh-
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