• 대한수학회지
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• 제45권5호
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• pp.1221-1241
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• 2008

Most of domains people have studied are convex bounded projective (or affine) domains. Edith $Soci{\acute{e}}$-$M{\acute{e}}thou$ [15] characterized ellipsoid in ${\mathbb{R}}^n$ by studying projective automorphism of convex body. In this paper, we showed convex and bounded projective domains can be identified from local data of their boundary points using scaling technique developed by several mathematicians. It can be found that how the scaling technique combined with properties of projective transformations is used to do that for a projective domain given local data around singular boundary point. Furthermore, we identify even unbounded or non-convex projective domains from its local data about a boundary point.

• 대한수학회보
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• 제56권4호
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• pp.929-937
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• 2019

The main purpose of this paper is to establish $H{\ddot{o}}lder$ estimates for the Cauchy transform in a class of finite/infinite type convex domains in $\mathbb{C}^2$.

• 대한수학회논문집
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• 제22권1호
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• pp.111-119
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• 2007

We consider the growth norm of a measurable function f defined by defined by $${\parallel}f{\parallel}-\sigma=ess\;sup\{\delta_D(z)^\sigma{\mid}f(z)\mid:z{\in}D\}$$, where $\delta_D(z)$ denote the distance from z to ${\partial}D$. We prove some kind of optimal growth norm estimates for a on convex domains.

• Journal of Electrical Engineering and Technology
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• 제12권1호
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• pp.72-77
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• 2017

This paper proposes the explicit tuning rule of multi-loop PID controller for brushless direct current motors to predict the system behaviors in time and frequency domains, using properties of the convex combination method. The convex set of the proposed controllers formulates the envelope to satisfy the performances in time and frequency domains. The final control parameters are determined by solving the convex optimization problem subject to the constraints which are represented as convex set of time domain performances. The effectiveness of the proposed control method is shown in the numerical simulation, in which controller tuning algorithm and dynamics of brushless DC motor are well taken into account.

• East Asian mathematical journal
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• 제31권3호
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• pp.351-356
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• 2015

In this paper, we study holomorphic discs in a domain with a plurisubharmonic peak function at a boundary point. The aim is to describe boundary behavior of holomorphic discs in convex finite type domains in the complex Euclidean space in term of a special local neigh-borhood system at a boundary point.

• Kyungpook Mathematical Journal
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• 제63권4호
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• pp.577-591
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• 2023

In this paper we establish the L^p boundedness of Marcinkiewicz integral operators on product domains with rough kernels satisfying a weak size condition. We assume that our kernels are supported on surfaces generated by curves more general than polynomials and convex functions. This generalizes and extends previous results.

• 대한수학회논문집
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• 제33권2호
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• pp.409-421
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• 2018

Let X be a complex manifold of dimension n $n{\geqslant}2$ and let ${\Omega}{\Subset}X$ be a weakly q-convex domain with smooth boundary. Assume that E is a holomorphic line bundle over X and $E^{{\otimes}m}$ is the m-times tensor product of E for positive integer m. If there exists a strongly plurisubharmonic function on a neighborhood of $b{\Omega}$, then we solve the ${\bar{\partial}}$-problem with support condition in ${\Omega}$ for forms of type (r, s), $s{\geqslant}q$ with values in $E^{{\otimes}m}$. Moreover, the solvability of the ${\bar{\partial}}_b$-problem on boundaries of weakly q-convex domains with smooth boundary in $K{\ddot{a}}hler$ manifolds are given. Furthermore, we shall establish an extension theorem for the ${\bar{\partial}}_b$-closed forms.

• 대한수학회보
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• 제46권5호
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• pp.823-833
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• 2009

It is well-known that if a convex hyperbolic polygon is constructed as a fundamental domain for a subgroup of the modular group, then its translates by the group elements form a locally finite tessellation and its side-pairing transformations form a system of generators for the group. Such hyperbolically convex polygons can be obtained by using Dirichlet's and Ford's polygon constructions. Another method of obtaining a fundamental domain for subgroups of the modular group is through the use of a right coset decomposition and we call such domains standard fundamental domains. In this paper we give subgroups of the modular group which do not have hyperbolically convex standard fundamental domain containing only inequivalent cusps.

• 대한수학회논문집
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• 제38권2호
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• pp.401-430
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• 2023

In this paper, we prove L^p estimates of a class of singular integral operators on product domains along surfaces defined by mappings that are more general than polynomials and convex functions. We assume that the kernels are in L(log L)² (𝕊^n-1 × 𝕊^m-1). Furthermore, we prove L^p estimates of the related class of Marcinkiewicz integral operators. Our results extend as well as improve previously known results.

• 대한수학회지
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• 제44권6호
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• pp.1417-1428
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• 2007

We obtain weighted $L^p$ estimates $(1{\leq}p<{\infty})\;for\;\bar{\partial}$ on convex domains with piecewise smooth boundaries in $\mathbb{C}^2$ by using explicit formulas of solutions introduced by Berndtsson and Andersson.