• Journal of the Chungcheong Mathematical Society
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• v.22 no.1
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• pp.117-121
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• 2009

For $1{\leq}p$, $q{\leq}{\infty}$ and $s{\in}\mathbb{R}$, it is proved that there exists a constant C > 0 such that for any $f{\in}B^{s+2}_{p,q}(\mathbb{R}^n)$ $${\parallel}f{\parallel}_{B^{s+2}_{p,q}(\mathbb{R}^n)}{\leq}C{\parallel}f\;-\;{\Delta}f{\parallel}_{B^{s}_{p,q}(\mathbb{R}^n)}$$, which tells us that the operator $I-\Delta$ is $B^{s+2}_{p,q}$-coercive on the Besov space $B^s_{p,q}$.

• Bulletin of the Korean Mathematical Society
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• v.56 no.6
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• pp.1643-1653
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• 2019

This paper shows that if $1<p<{\infty}$, ${\alpha}{\geq}-n-2$, ${\alpha}>-1-{\frac{p}{2}}$ and f is holomorphic on the unit ball ${\mathbb{B}}_n$, then $${\int_{{\mathbb{B}}_n}}{\mid}Rf(z){\mid}^p(1-{\mid}z{\mid}^2)^{p+{\alpha}}dv_{\alpha}(z)<{\infty}$$ if and only if $${\int_{{\mathbb{B}}_n}}{\int_{{\mathbb{B}}_n}}{\frac{{\mid}f(z)-F({\omega}){\mid}^p}{{\mid}1-(z,{\omega}){\mid}^{n+1+s+t-{\alpha}}}}(1-{\mid}{\omega}{\mid}^2)^s(1-{\mid}z{\mid}^2)^tdv(z)dv({\omega})<{\infty}$$ where s, t > -1 with $min(s,t)>{\alpha}$.

• Kyungpook Mathematical Journal
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• v.64 no.2
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• pp.271-286
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• 2024

In this paper, we prove the existence of distributional solutions in the anisotropic Sobolev space $\mathring{W}^{1,\overrightarrow{p}(\cdot)}(\Omega)$ with variable exponents and zero boundary, for a class of variable exponents anisotropic nonlinear elliptic equations having a compound nonlinearity $G(x, u)=\sum_{i=1}^{N}(\left|f\right|+\left|u\right|)^{p_i(x)-1}$ on the right-hand side, such that f is in the variable exponents anisotropic Lebesgue space $L^{\vec{p}({\cdot})}(\Omega)$, where $\vec{p}({\cdot})=(p_1({\cdot}),{\ldots},p_N({\cdot})){\in}(C(\bar{\Omega},]1,+{\infty}[))^N$.

• Bulletin of the Korean Mathematical Society
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• v.55 no.4
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• pp.1103-1107
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• 2018

Let M be a complete spacelike hypersurface in the (n + 1)-dimensional Minkowski space ${\mathbb{L}}^{n+1}$. Suppose that every unit speed curve X(s) on M satisfies ${\langle}X^{\prime\prime}(s),X^{\prime\prime}s){\rangle}{\geq}-1/r^2$ and there exists a point $p{\in}M$ such that for every unit speed geodesic X(s) of M through the point p, ${\langle}X^{\prime\prime}(s),X^{\prime\prime}s){\rangle}=-1/r^2$ holds. Then, we show that up to isometries of ${\mathbb{L}}^{n+1}$, M is the hyperbolic space $H^n(r)$.

• Communications of the Korean Mathematical Society
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• v.10 no.1
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• pp.207-213
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• 1995

Let $(\Omega, F, P)$ be a probability space with F a $\sigma$-algebra of subsets of the measure space $\Omega$ and P a probability measure on $\Omega$. Suppose $a > 0$ and let $(F_t)_{t \in [0,a]}$ be an increasing family of sub-$\sigma$-algebras of F. If $r > 0$, let $J = [-r,0]$ and $C(J, R^n)$ the Banach space of all continuous paths $\gamma : J \to R^n$ with the sup-norm $\Vert \gamma \Vert = sup_{s \in J}$\mid$\gamma(s)$\mid$$ where $$\mid$\cdot$\mid$$ denotes the Euclidean norm on $R^n$. Let E,F be separable real Banach spaces and L(E,F) be the Banach space of all continuous linear maps $T : E \to F$.

• Journal of the Chungcheong Mathematical Society
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• v.22 no.3
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• pp.481-495
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• 2009

Huffman, Park and Skoug introduced various results for the $L_{p}$ analytic Fourier-Feynman transform and the convolution for functionals on classical Wiener space which belong to some Banach algebra $\mathcal{S}$ introduced by Cameron and Storvick. Also Chang, Kim and Yoo extended the above results to an abstract Wiener space for functionals in the Fresnel class $\mathcal{F}(B)$ which corresponds to $\mathcal{S}$. Moreover they introduced the $L_{p}$ analytic Fourier-Feynman transform for functionals on a product abstract Wiener space and then established the above results for functionals in the generalized Fresnel class $\mathcal{F}_{A1,A2}$ containing $\mathcal{F}(B)$. In this paper, we investigate more generalized relationships, between the Fourier-Feynman transform and the convolution product for functionals in $\mathcal{F}_{A1,A2}$, than the above results.

• Communications of the Korean Mathematical Society
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• v.9 no.3
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• pp.731-737
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• 1994

Let $(\Omega, F, P)$ be a probability space with F a $\sigma$-algebra of subsets of the measure space $\Omega$ and P a probability measures on $\Omega$. Suppose $a > 0$ and let $(F_t)_{t \in [0,a]}$ be an increasing family of sub-$\sigma$- algebras of F. If $r > 0$, let $J = [-r, 0]$ and $C(J, R^n)$ the Banach space of all continuous paths $\gamma : J \to R^n$ with the sup-norm $\Vert \gamma \Vert_C = sup_{s \in J} $\mid$\gamma(x)$\mid$$ where $$\mid$\cdot$\mid$$ denotes the Euclidean norm on $R^n$. Let E and F be separable real Banach spaces and L(E,F) be the Banach space of all continuous linear maps $T : E \to F$ with the norm $\Vert T \Vert = sup {$\mid$T(x)$\mid$_F : x \in E, $\mid$x$\mid$_E \leq 1}$.

• Journal of the Korean Mathematical Society
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• v.31 no.3
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• pp.467-475
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• 1994

In 1983 Harmand and Lima [5] proved that if X is a Banach space for which K(X), the space of compact linear operators on X, is an M-ideal in L(X), the space of bounded linear operators on X, then it has the metric compact approximation property. A strong converse of the above result holds if X is a closed subspace of either $\elll_p(1 < p < \infty) or c_0 [2,15]$. In 1979 J. Johnson [7] actually proved that if X is a Banach space with the metric compact approximation property, then the annihilator K(X)^\bot$ of K(X) in $L(X)^*$ is the kernel of a norm-one projection in $L(X)^*$, which is the case if K(X) is an M-ideal in L(X).

• Communications of the Korean Mathematical Society
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• v.22 no.4
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• pp.527-534
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• 2007

This paper deals with the BK-AK property of the integrated rate space ${\int}{\ell}_{\pi}$. Importance of ${\delta}^{(k)}$ in this content is pointed out. We investigate a determining set for the integrated rate space ${\int}{\ell}_{\pi}$. The set of all infinite matrices transforming ${\int}{\ell}_{\pi}$, into BK-AK space Y is denoted $({\int}{\ell}_{\pi}:\;Y)$. We characterize the classes $({\int}{\ell}_{\pi}:\;Y)$. When $Y={\ell}_{\infty},\;c_0,\;c,\;{\ell}^p,\;bv,\;bv_0,\;bs,\;cs,\;{\ell}_p,\;{\ell}_{\pi}$. In summary we have the following table:

• Proceedings of the Korea Association of Information Systems Conference
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• 2004.11a
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• pp.312-326
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• 2004

본 연구는 Virtual Space의 수용에 어떻게 영향을 미치는지를 파악하고자 하는 연구이다. 이 연구는 정보기술수용 모형의 확장모형인 TAM2(Venkatesh & Davis, 2000)를 적용하여 연구하였으며, 실제 Virtual Space를 사용한 경험이 있는 사용자를 대상으로 설문하여 SPSS와 AMOS를 이용하여 TAM2 모형을 검증하고자 하였다. 연구결과 정보기술 수용에 대한 대상이 조직 내부의 이용자로 연구했던 TAM2와 다르게 외부변수 중 직무관련성과 결과 품질에 대한 변수가 유의하지 않은 것으로 나타났다. 하지만 주관적 규범, 이미지, 결과 논증가능성 등은 유용성에 정의 영향을 주었으며, 특히 외부 변수 중 주관적 규범은 매우 큰 영향을 주고 있는 것으로 나타나 새로운 정보기술의 수용에 있어 중요한 요인으로 분석되었다. 본 연구 결과의 시사점과 한계점 및 향후 연구방향을 결론에서 제시하였다.