• The Pure and Applied Mathematics
• /
• v.23 no.1
• /
• pp.61-72
• /
• 2016

In this paper, a boundary version of the Schwarz lemma for the holom- rophic function satisfying f(a) = b, |a| < 1, b ∈ ℂ and ℜf(z) > α, 0 ≤ α < |b| for |z| < 1 is invetigated. Also, we estimate a modulus of the angular derivative of f(z) function at the boundary point c with ℜf(c) = a. The sharpness of these inequalities is also proved.

• Journal of the Korean Mathematical Society
• /
• v.33 no.2
• /
• pp.399-411
• /
• 1996

Let $\Omega$ be a smoothly bounded pseudoconvex domain in $C^n$ and let $A(\Omega)$ denote the functions holomorphic on $\Omega$ and continuous on $\bar{\Omega}$. A point $p \in b\Omega$ is a peak point if there is a function $f \in A(\Omega)$ such that $f(p) = 1, and $\mid$f(z)$\mid$ < 1 for z \in \bar{\Omega} - {p}$.

• Communications of the Korean Mathematical Society
• /
• v.10 no.2
• /
• pp.349-355
• /
• 1995

Let $D \subset C^n$ be a smoothly bounded pseudoconvex domain and let ${\bar{D}_r}_r$ be a family of smooth perturbations of $\bar{D}$ such that $\bar{D} \subset \bar{D}_r$. Let $K_D(z, w)$ be the Bergman kernel function on $D \times D$. Then $lim_{r \to 0} K_{D_r}(z, w) = K_D(z, w)$ locally uniformally on $D \times D$.

• Communications of the Korean Mathematical Society
• /
• v.10 no.4
• /
• pp.867-874
• /
• 1995

Linear invariance is closely related to the concept of uniform local univalence. We give a geometric proof that a holomorphic locally univalent function defined on the open unit disk is linearly invariant if and only if it is uniformly locally univalent.

• Communications of the Korean Mathematical Society
• /
• v.21 no.4
• /
• pp.719-727
• /
• 2006

In this paper, we study the boundedness and the com-pactness of weighted composition operator between $H^{\infty}$ and Bergman type space on the unit ball of $\mathbb{C}^n$. Also, the norm of corresponding weighted composition operator is computed.

• Bulletin of the Korean Mathematical Society
• /
• v.48 no.6
• /
• pp.1119-1124
• /
• 2011

In the present paper, we study the chaotic property of weighted composition operators acting on the holomorphic function space $H(\mathbb{U})$.

• Bulletin of the Korean Mathematical Society
• /
• v.50 no.6
• /
• pp.2053-2059
• /
• 2013

In this paper, a boundary version of the Schwarz lemma is investigated. We obtain more general results at the boundary. Also, new inequalities of the Schwarz lemma at boundary is obtained and the sharpness of these inequalities is proved.

• Honam Mathematical Journal
• /
• v.43 no.3
• /
• pp.385-402
• /
• 2021

The geometry of Poincaré disk itself is interpreted without any mapping to different spaces. Our approach might be one of the shortest and is intended for educational contribution.

• Journal of the Chungcheong Mathematical Society
• /
• v.35 no.4
• /
• pp.277-295
• /
• 2022

The author proved a modular transformation formula for a function related to generalized non-holomorphic Eisenstein series and, using this formula, established a lot of infinite series identities. In this paper, we find more generalized series relations which contain the author's previous work.

• Journal of the Korean Mathematical Society
• /
• v.52 no.5
• /
• pp.945-954
• /
• 2015

Let ${\lambda}_f(n)$ denote the n-th normalized Fourier coefficient of a primitive holomorphic form f for the full modular group ${\Gamma}=SL_2({\mathbb{Z}})$. In this paper, we are concerned with ${\Omega}$-result on the summatory function ${\sum}_{n{\leqslant}x}{\lambda}^2_f(n^2)$, and establish the following result ${\sum}_{\leqslant}{\lambda}^2_f(n^2)=c_1x+{\Omega}(x^{\frac{4}{9}})$, where $c_1$ is a suitable constant.