59 research outputs found
단위구상의 bergman 공간들에 대한 carleson 측도
No full text학위논문(석사) - 한국과학기술원 : 응용수학과, 1990.2, [ [ii], 16, [2] p. ; ]A characterization of Carleson measures for the Bergman spaces on the ball Let E() denote the pseudo-hyperbolic disc of the unit disc D of the complex plane C. It is known that if and is a positive finite Borel measure on D, then the following two quantities are equivalent: \begin{eqnarray*}(i)& & \sup \{\int_D \mid f \mid^p d\mu/ \parallel f \parallel^p_{A^p} : f \in A^p(D),\; f \not\equiv 0 \}\\ (ii)& & \sup \{\mu(E(w,r))/m(E(w,r)) : w \in D \} \end{eqnarray*}\\ Where (D) denotes the Bergman space on D and m denotes the area measure on D. In this thesis, we extend this result to the unit ball of C.한국과학기술원 : 응용수학과
M-불변 laplacian에 관한 연구
No full text학위논문(석사) - 한국과학기술원 : 수학과, 1991.2, [ [ii], 13 p. ; ]Let B be the open unit ball of C, and let be the ordinary Laplacian. Then it is easily proved that if f is a holomfunction in B such that f(z),for all zB and on B, , then f must be constant. In this thesis, we prove an analogous result for the M-invariant Laplacian, , where M is the group of biholomorphic selfmaps of B.한국과학기술원 : 수학과
Bergman 공간상의 carleson 측도의 분류와 그 응용
No full text학위논문(석사) - 한국과학기술원 : 수학과, 1995.2, [ [ii], 22 p. ]Let U be the open unit disk with the normalized Lebesgue measure m and . For a positive measure μ on U and p ＞ 1, there exists a constant C satisfying
if and only if μ is a Carlson measure.
For 0 ＜ q ＜ p, Luecking found a necessary and sufficient condition for there to exist a constant C satisfying
In this paper we generalized this to the higher dimensional spaces and found some applications.한국과학기술원 : 수학과
Pluriharmonic 기호를 갖는 교환하는 toeplitz 연산자에 관한 연구
No full text학위논문(석사) - 한국과학기술원 : 수학과, 1991.2, [ [ii], 21 p. ; ]It has been recently proved by Sheldon Axler and Zeljko Cuckovic that on the Bergman space of the unit disc of the complex plane, two Toeplitz operator with harmonic symbols commute only in the obvious cases. In this thesis, we investigate the corresponding problem with pluriharmonic symbols on the higher dimensional situation. We first obtain a necessary condition and a sufficient condition for two commuting Toeplitz operators with pluriharmonic symbols on the Bergman space of the unit ball of higher dimensional complex space. As an application we show that if one of symbols in consideration is holomorphic or antiholomorphic, then so is the other. Our proof depends on a recent theorem of P. Ahern and W. Rudin concerning M-harmonic products.한국과학기술원 : 수학과
단위구 상의 Bloch 함수에 대한 Schwarz-Pick Type 부등식
No full text학위논문(석사) - 한국과학기술원 : 수학과 복소해석전공, 1994.2, [ 11 p. ; ]In this thesis, we proved Schwarz-Pick type inequality for Bloch functions in the unit ball of which is
◁수식 삽입▷(원문을 참조하세요)한국과학기술원 : 수학과 복소해석전공
Bergman 공간 위의 Toeplitz 작용소에 관한 연구
No full text학위논문(박사) - 한국과학기술원 : 수학과(복소해석학전공), 1994.2, [ 94 p. ; ]In this thesis, we are concerned with Toeplitz operators acting on the Bergman spaces of the unit ball in the n-dimensional complex space . The main purpose of the thesis is on the size estimate of the Toeplitz operators. More precisely, we mainly study the relationship between operator theoretic properties of Toeplitz operators and function theoretic properties of their symbols.
In Chapter 1, we consider the commuting problem for Toeplitz operators acting on the -Bergman space. In the one dimensional case, Axler and Cuckovic has recently showed that two Toeplitz operators with bounded harmonic symbols commute only in the obvious case. In this chapter, we consider the same problem with bounded pluriharmonic symbols on the ball and partially extend the Axler and Cuckovic result to the ball.
In Chapter 2, we consider the characterization problem of compact Toeplitz operators on the -Bergman space of a product of balls rather than the ball. In the ball or the polydisk setting, Zheng has recently characterized bounded symbols of compact Toeplitz operators in terms of certain boundary vanishing properties. In this chapter, we use a new argument to extend Zheng``s result to general product of balls, and obtain a new characterization and show that a certain restriction in Zheng``s characterization is inessential.
In Chapter 3, we introduce a Banach space of holomorphic functions on the ball motivated by the atomic decompositions in the sense of Luecking, and establish its dual and predual spaces. At the same time, we describe these spaces in terms of boundedness, compactness and membership in the Schatten p-classes of certain Toeplitz operators acting on the -Bergman space of the ball.
In Chapter 4, we consider a spectral property of Toeplitz operators acting on -Bergman space of the ball. In one dimensional setting, Zeng has considered a symbol continuous up to boundary and computed the essential spectrum of the corresponding Toeplitz ope...한국과학기술원 : 수학과(복소해석학전공)
Bloch 공간의 특성에 관한 연구
No full text학위논문(석사) - 한국과학기술원 : 수학과(복소해석 전공), 1994.8, [ 11 p. ; ]In the setting of the unit disk, it is recently known that the following norms are equivalent: For any given p (0, ) and \verepsilon \in (0, 1), (a) . (b) \sup_{\verepsilon < \mid a mid < 1} \parallel f(\alpha + (1 - \mid a \mid \cdot)-f(\alpha) \parallel_p. In this paper we generalized this to the higher dimensional space.한국과학기술원 : 수학과(복소해석 전공)
단위구상의 해석함수의 경계치에 대한 연구
No full text학위논문(석사) - 한국과학기술원 : 응용수학과, 1990.2, [ [ii], 17, [2] p. ; ]한국과학기술원 : 응용수학과
Double integral characterizations of harmonic Bergman spaces
No full textAbstractRecently Li et al. have characterized, except for a critical case, the weighted Bergman spaces over the complex ball by means of integrability conditions of double integrals associated with difference quotients of holomorphic functions. In this paper we extend those characterizations to the case of weighted harmonic Bergman spaces over the real ball and complement their results by providing a characterization for the missing critical case. We also investigate the possibility of extensions to the half-space setting. Our observations reveal an interesting half-space phenomenon caused by the unboundedness of the half-space
Cauchy integral equalities and applications
No full textWe study bounded holomorphic functions
π
\pi
on the unit ball
B
n
{B_n}
of
C
n
{\mathbb {C}^n}
satisfying the following so-called Cauchy integral equalities:
C
[
π
m
+
1
π
¯
]
=
γ
m
π
m
a
m
p
;
(
m
=
0
,
1
,
2
,
…
)
\begin {array}{*{20}{c}} {C[{\pi ^{m + 1}}\bar \pi ] = {\gamma _m}{\pi ^m}} & {(m = 0,1,2, \ldots )} \\ \end {array}
for some sequence
γ
m
{\gamma _m}
depending on
π
\pi
. Among the applications are the Ahern-Rudin problem concerning the composition property of holomorphic functions on
B
n
{B_n}
, a projection theorem about the orthogonal projection of
H
2
(
B
n
)
{H^2}({B_n})
onto the closed subspace generated by holomorphic polynomials in
π
\pi
, and some new information about the inner functions. In particular, it is shown that if we interpret
BMOA
(
B
n
)
{\text {BMOA}}({B_n})
as the dual of
H
1
(
B
n
)
{H^1}({B_n})
, then the map
g
→
g
∘
π
g \to g \circ \pi
is a linear isometry of
BMOA
(
B
1
)
{\text {BMOA}}({B_1})
into
BMOA
(
B
n
)
{\text {BMOA}}({B_n})
for every inner function
π
\pi
on
B
n
{B_n}
such that
π
(
0
)
=
0
\pi (0) = 0
.</p
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