• Bulletin of the Korean Mathematical Society
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• v.53 no.1
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• pp.153-161
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• 2016

It is shown that the algebra $\mathfrak{H}^{\infty}$ of bounded Dirichlet series is not a coherent ring, and has infinite Bass stable rank. As corollaries of the latter result, it is derived that $\mathfrak{H}^{\infty}$ has infinite topological stable rank and infinite Krull dimension.

• Bulletin of the Korean Mathematical Society
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• v.55 no.6
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• pp.1659-1666
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• 2018

Let $P_r$ denote an almost-prime with at most r prime factors, counted according to multiplicity. In this paper, it is proved that for every sufficiently large even integer N, the equation $$N=x^2+p_1^2+p_2^3+p_3^3+p_4^4+p_5^4$$ is solvable with x being an almost-prime $P_4$ and the other variables primes. This result constitutes an improvement upon that of $L{\ddot{u}}$ [7].

• Journal of the Korean Mathematical Society
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• v.32 no.4
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• pp.697-712
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• 1995

In the present article we consider multiparameter maximal averages and discover the crucial roles played by the number of parameters in their boundedness properties. The problem we shall deal with is initiated by Rubio de Francia [8] and will be in the spirit of an inductive extension to multiparameter cases, in which tools of our study rely on the theory of Harmonic Analysis on product spaces. Suppose that $d_\mu$ is a complex Borel measure supported on a compact subset S of $R^N$ having total mass one, $\smallint_S d_\mu = 1$.

• Communications of the Korean Mathematical Society
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• v.24 no.2
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• pp.187-195
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• 2009

We investigate the boundary values of the holomorphic mean Lipschitz function. In fact, we prove that the admissible limit exists at every boundary point of the unit ball for the holomorphic mean Lipschitz functions under some assumptions on the Lipschitz order. Moreover, we get embedding theorems of holomorphic mean Lipschitz spaces into Hardy spaces or into the Bloch space on the unit ball in $\mathbb{C}_n$.

• Journal of the Korean Mathematical Society
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• v.53 no.4
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• pp.847-868
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• 2016

Let M be an invariant subspace of $H^2$ over the bidisk. Associated with M, we have the fringe operator $F^M_z$ on $M{\ominus}{\omega}M$. It is studied the Fredholmness of $F^M_z$ for (generalized) zero based invariant subspaces M. Also ker $F^M_z$ and ker $(F^M_z)^*$ are described.

• Journal of the Korean Mathematical Society
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• v.31 no.4
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• pp.703-707
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• 1994

Since John and Nirenberg introduced the BMO in early 1960 [JN], it has been one of the most significant function spaces. The significance of BMO lies in the fact that BMO is a limiting space of $L^p (p \longrightarrow \infty)$, or a proper substitute of $L^\infty$. A dual statement of this would be that the Hardy space $H^1$ is a proper substitute of $L^1$.

• Review of KIISC
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• v.2 no.4
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• pp.30-36
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• 1992

이 논문에서 우리는 여러 가지 분할 항등식을 유도했고 제한된 분할에 관한 새로운 항등식을 증명하고, 분할의 기본적인 이론과 분할함수(Partition Number Function)가 다항식 함수가 아니라는 것을 보이며, n 의 분할의 수 p(n)에 대한 하계(Lower Bound)를 얻기 위해 Stirling의 n ! 에 대한 근사값을 소개한다. 그리고 Hardy-Ramanujan 공식, Euler 항등식과 p(n) 의 순환식을 유도하며, 그리고 $d_m$(n)이n을m개의 부분으로 분할하는 분할의 수를 나타낼 때 우리는 $d_m$(n)에 관한 일반적인 공식을 p(n)과 함께 행렬식의 형태로 표현한다.

• Review of KIISC
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• v.2 no.4
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• pp.37-47
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• 1992

이 논문에서 우리는 여러 가지 분할 항등식을 유도했고 제한된 분할에 관한 새로운 항등식을 증명하고, 분할의 기본적인 이론과 분할함수(Partition Number Function)가 다항식 함수가 아니라는 것을 보이며, n의 분할의 수 p(n)에 대한 ㅎ계(Lower Bound)를 얻기 위해 Stirling의 n !에 대한 근사값을 소개한다. 그리고Hardy-Ramanujan 공식, Euler 항등식과 p(n)의 순환식을 유도하며, 그리고 d$_{m}$ (n)이 n을 m개의 부분으로 분할하는 분할의 수를 나타낼 때 우리는 d$_{m}$ (n) 에 관한 일반적인 공식을 p(n)과 함께 행렬식의 형태로 표현한다.

• East Asian mathematical journal
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• v.21 no.1
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• pp.41-48
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• 2005

In this paper we first introduce a space of homogeneous type X, and then consider a kind of generalized upper half-space $X{\times}(0,\;\infty)$. We are mainly considered with inequalities for the $L^p$ norms of area functions associated with approach regions in $X{\times}(0,\;\infty)$.

• Progress in Superconductivity
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• v.2 no.1
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• pp.11-14
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• 2000

The notion of the finite pairing interaction energy range Td is shown to result in a linear temperature dependence of the London magnetic penetration depth length, ${\Delta}{\lambda}{/\lambda}(0)=(T/Td)2/\pi)ln2$ at low T in the case of the s-wave pairing state, accounting for data of high Tc superconductor by Hardy et al.