• Journal of the Chungcheong Mathematical Society
• /
• v.10 no.1
• /
• pp.17-22
• /
• 1997

Let B be the open unit ball in the complex space $\mathbb{C}^n$. A holomorphic function $f:B{\rightarrow}C$ which satisfies sup{(1- ${\parallel}\;{\nabla}_zf\;{\parallel}\;{\mid}z{\in}B$} < $+{\infty}$ is called Bloch type function. In this paper, we will find some integral representation of Bloch type functions.

• Journal of the Korean Mathematical Society
• /
• v.51 no.1
• /
• pp.125-135
• /
• 2014

We study the compact intertwining relations for composition operators, whose intertwining operators are Volterra type operators from the weighted Bergman spaces to the weighted Bloch spaces in the unit disk. As consequences, we find a new connection between the weighted Bergman spaces and little weighted Bloch spaces through this relations.

• Communications of the Korean Mathematical Society
• /
• v.22 no.3
• /
• pp.373-382
• /
• 2007

In this paper, we characterize the boundedness and compactness of weighted composition operators ${\psi}C{\varphi}f=\psi(f^{\circ}\varphi)$ acting between Bergman and Bloch spaces of holomorphic functions on the open unit disk D.

• Bulletin of the Korean Mathematical Society
• /
• v.54 no.4
• /
• pp.1337-1346
• /
• 2017

We define Bloch-type spaces of ${\mathcal{C}}^1({\mathbb{H}})$ on the upper half plane H and characterize them in terms of weighted Lipschitz functions. We also discuss the boundedness of a composition operator ${\mathcal{C}}_{\phi}$ acting between two Bloch spaces. These obtained results generalize the corresponding known ones to the setting of upper half plane.

• Journal of the Chungcheong Mathematical Society
• /
• v.20 no.3
• /
• pp.203-210
• /
• 2007

Let X be a hyperbolic region in the complex plane C such that the hyperbolic metrix ${\lambda}_X(w){\mid}dw{\mid}$ exists. Let $R(X)=sup\{{\delta}_X(w):w{\in}X\}$ where ${\delta}_X(w)$ is the euclidean distance from w to ${\partial}X$. Here ${\partial}X$ is the boundary of X. A hyperbolic region X is called a Bloch region if R(X) < ${\infty}$. In this paper, we obtain lower bounds for the hyperbolic metric on Bloch regions in terms of the distance to the boundary.

• 한국정보디스플레이학회:학술대회논문집
• /
• 2005.07a
• /
• pp.493-495
• /
• 2005

The director profiles of the Bloch walls are directly visualized using fluorescence confocal polarizing microscopy. Both pure twist Bloch walls and diffuse Bloch walls are analyzed. Polar anchoring energy was measured from optical simulation of the transmitted light interference pattern or the fluorescence intensity profile of a pure twist wall..

• The Pure and Applied Mathematics
• /
• v.5 no.1
• /
• pp.17-21
• /
• 1998

In [5], Zhu introduces a bounded operator T from $L^{\infty}$(D) into Bloch space B. In this paper, we will consider the generalized Bloch spaces $B_{q}$ and find bounded operator from $L^{\infty}$(D) into $B_{q}$.

• Bulletin of the Korean Mathematical Society
• /
• v.58 no.2
• /
• pp.481-495
• /
• 2021

In this paper, we investigate the properties of Bergman spaces, Bloch spaces and integral means of p-harmonic functions on the unit ball in ℝn. Firstly, we offer some Lipschitz-type and double integral characterizations for Bergman space ��kγ. Secondly, we characterize Bloch space ��αω in terms of weighted Lipschitz conditions and BMO functions. Finally, a Hardy-Littlewood type theorem for integral means of p-harmonic functions is established.

• Honam Mathematical Journal
• /
• v.37 no.4
• /
• pp.387-395
• /
• 2015

We investigate conditions under which a holomorphic self-map of the unit disk induces a bounded composition operator and study some properties of the composition operator from the Bloch-type spaces into a generalization of the Bloch-type spaces.

• Journal of the Korean Mathematical Society
• /
• v.54 no.2
• /
• pp.627-645
• /
• 2017

In this paper, we characterize the boundedness, compactness and essential norm of products of differentiation and composition operators from the Bloch space and weighted Dirichlet spaces to analytic Morrey type spaces.